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distributions</title> <meta name="description" content="Search results for: multivariate distributions"> <meta name="keywords" content="multivariate distributions"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="multivariate distributions"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1300</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: multivariate distributions</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1300</span> Regression for Doubly Inflated Multivariate Poisson Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ishapathik%20Das">Ishapathik Das</a>, <a href="https://publications.waset.org/abstracts/search?q=Sumen%20Sen"> Sumen Sen</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Rao%20Chaganty"> N. Rao Chaganty</a>, <a href="https://publications.waset.org/abstracts/search?q=Pooja%20Sengupta"> Pooja Sengupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=copula" title="copula">copula</a>, <a href="https://publications.waset.org/abstracts/search?q=Gaussian%20copula" title=" Gaussian copula"> Gaussian copula</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions" title=" multivariate distributions"> multivariate distributions</a>, <a href="https://publications.waset.org/abstracts/search?q=inflated%20distributios" title=" inflated distributios"> inflated distributios</a> </p> <a href="https://publications.waset.org/abstracts/105114/regression-for-doubly-inflated-multivariate-poisson-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/105114.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">156</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1299</span> The Modality of Multivariate Skew Normal Mixture</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bader%20Alruwaili">Bader Alruwaili</a>, <a href="https://publications.waset.org/abstracts/search?q=Surajit%20Ray"> Surajit Ray</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Finite mixtures are a flexible and powerful tool that can be used for univariate and multivariate distributions, and a wide range of research analysis has been conducted based on the multivariate normal mixture and multivariate of a t-mixture. Determining the number of modes is an important activity that, in turn, allows one to determine the number of homogeneous groups in a population. Our work currently being carried out relates to the study of the modality of the skew normal distribution in the univariate and multivariate cases. For the skew normal distribution, the aims are associated with studying the modality of the skew normal distribution and providing the ridgeline, the ridgeline elevation function, the $\Pi$ function, and the curvature function, and this will be conducive to an exploration of the number and location of mode when mixing the two components of skew normal distribution. The subsequent objective is to apply these results to the application of real world data sets, such as flow cytometry data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mode" title="mode">mode</a>, <a href="https://publications.waset.org/abstracts/search?q=modality" title=" modality"> modality</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20skew%20normal" title=" multivariate skew normal"> multivariate skew normal</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20mixture" title=" finite mixture"> finite mixture</a>, <a href="https://publications.waset.org/abstracts/search?q=number%20of%20mode" title=" number of mode"> number of mode</a> </p> <a href="https://publications.waset.org/abstracts/68912/the-modality-of-multivariate-skew-normal-mixture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68912.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">488</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1298</span> Modelling Operational Risk Using Extreme Value Theory and Skew t-Copulas via Bayesian Inference </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Betty%20Johanna%20Garzon%20Rozo">Betty Johanna Garzon Rozo</a>, <a href="https://publications.waset.org/abstracts/search?q=Jonathan%20Crook"> Jonathan Crook</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Moreira"> Fernando Moreira</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=operational%20risk" title="operational risk">operational risk</a>, <a href="https://publications.waset.org/abstracts/search?q=loss%20distribution%20approach" title=" loss distribution approach"> loss distribution approach</a>, <a href="https://publications.waset.org/abstracts/search?q=extreme%20value%20theory" title=" extreme value theory"> extreme value theory</a>, <a href="https://publications.waset.org/abstracts/search?q=copulas" title=" copulas"> copulas</a> </p> <a href="https://publications.waset.org/abstracts/19385/modelling-operational-risk-using-extreme-value-theory-and-skew-t-copulas-via-bayesian-inference" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19385.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">603</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1297</span> A Proposed Mechanism for Skewing Symmetric Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20T.%20Alodat">M. T. Alodat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a mechanism for skewing any symmetric distribution. The new distribution is called the deflation-inflation distribution (DID). We discuss some statistical properties of the DID such moments, stochastic representation, log-concavity. Also we fit the distribution to real data and we compare it to normal distribution and Azzlaini's skew normal distribution. Numerical results show that the DID fits the the tree ring data better than the other two distributions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=normal%20distribution" title="normal distribution">normal distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=moments" title=" moments"> moments</a>, <a href="https://publications.waset.org/abstracts/search?q=Fisher%20information" title=" Fisher information"> Fisher information</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20distributions" title=" symmetric distributions"> symmetric distributions</a> </p> <a href="https://publications.waset.org/abstracts/28593/a-proposed-mechanism-for-skewing-symmetric-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28593.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">659</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1296</span> Multivariate Genome-Wide Association Studies for Identifying Additional Loci for Myopia </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qiao%20Fan">Qiao Fan</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaobo%20Guo"> Xiaobo Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Junxian%20Zhu"> Junxian Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaohu%20Ding"> Xiaohu Ding</a>, <a href="https://publications.waset.org/abstracts/search?q=Ching-Yu%20Cheng"> Ching-Yu Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Tien-Yin%20Wong"> Tien-Yin Wong</a>, <a href="https://publications.waset.org/abstracts/search?q=Mingguang%20He"> Mingguang He</a>, <a href="https://publications.waset.org/abstracts/search?q=Heping%20Zhang"> Heping Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Xueqin%20Wang"> Xueqin Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A systematic, simultaneous analysis of multiple phenotypes in genome-wide association studies (GWASs) draws a great attention to integrate the signals from single phenotypes with increased power. However, lacking an interpretable and efficient multivariate GWAS analysis impede the application of such approach. In this study, we propose to decompose the multivariate model into a series of simple univariate models. This transformation illuminates what exactly the individual trait contributes to the significant signals from the multivariate analyses. By employing our approach in the analysis of three myopia-related endophenotypes from the Singapore Malay Eye Study (SIMES), we identify novel candidate loci which were successfully validated in an independent Guangzhou Twin Eye Study (GTES). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=GWAS%20multivariate" title="GWAS multivariate">GWAS multivariate</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20traits" title=" multiple traits"> multiple traits</a>, <a href="https://publications.waset.org/abstracts/search?q=myopia" title=" myopia"> myopia</a>, <a href="https://publications.waset.org/abstracts/search?q=association" title=" association"> association</a> </p> <a href="https://publications.waset.org/abstracts/79085/multivariate-genome-wide-association-studies-for-identifying-additional-loci-for-myopia" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79085.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1295</span> Beyond Classic Program Evaluation and Review Technique: A Generalized Model for Subjective Distributions with Flexible Variance</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Byung%20Cheol%20Kim">Byung Cheol Kim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Program Evaluation and Review Technique (PERT) is widely used for project management, but it struggles with subjective distributions, particularly due to its assumptions of constant variance and light tails. To overcome these limitations, we propose the Generalized PERT (G-PERT) model, which enhances PERT by incorporating variability in three-point subjective estimates. Our methodology extends the original PERT model to cover the full range of unimodal beta distributions, enabling the model to handle thick-tailed distributions and offering formulas for computing mean and variance. This maintains the simplicity of PERT while providing a more accurate depiction of uncertainty. Our empirical analysis demonstrates that the G-PERT model significantly improves performance, particularly when dealing with heavy-tail subjective distributions. In comparative assessments with alternative models such as triangular and lognormal distributions, G-PERT shows superior accuracy and flexibility. These results suggest that G-PERT offers a more robust solution for project estimation while still retaining the user-friendliness of the classic PERT approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=PERT" title="PERT">PERT</a>, <a href="https://publications.waset.org/abstracts/search?q=subjective%20distribution" title=" subjective distribution"> subjective distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=project%20management" title=" project management"> project management</a>, <a href="https://publications.waset.org/abstracts/search?q=flexible%20variance" title=" flexible variance"> flexible variance</a> </p> <a href="https://publications.waset.org/abstracts/192135/beyond-classic-program-evaluation-and-review-technique-a-generalized-model-for-subjective-distributions-with-flexible-variance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192135.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">18</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1294</span> Copula Markov Switching Multifractal Models for Forecasting Value-at-Risk </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Giriraj%20Achari">Giriraj Achari</a>, <a href="https://publications.waset.org/abstracts/search?q=Malay%20Bhattacharyya"> Malay Bhattacharyya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the effectiveness of Copula Markov Switching Multifractal (MSM) models at forecasting Value-at-Risk of a two-stock portfolio is studied. The innovations are allowed to be drawn from distributions that can capture skewness and leptokurtosis, which are well documented empirical characteristics observed in financial returns. The candidate distributions considered for this purpose are Johnson-SU, Pearson Type-IV and α-Stable distributions. The two univariate marginal distributions are combined using the Student-t copula. The estimation of all parameters is performed by Maximum Likelihood Estimation. Finally, the models are compared in terms of accurate Value-at-Risk (VaR) forecasts using tests of unconditional coverage and independence. It is found that Copula-MSM-models with leptokurtic innovation distributions perform slightly better than Copula-MSM model with Normal innovations. Copula-MSM models, in general, produce better VaR forecasts as compared to traditional methods like Historical Simulation method, Variance-Covariance approach and Copula-Generalized Autoregressive Conditional Heteroscedasticity (Copula-GARCH) models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Copula" title="Copula">Copula</a>, <a href="https://publications.waset.org/abstracts/search?q=Markov%20Switching" title=" Markov Switching"> Markov Switching</a>, <a href="https://publications.waset.org/abstracts/search?q=multifractal" title=" multifractal"> multifractal</a>, <a href="https://publications.waset.org/abstracts/search?q=value-at-risk" title=" value-at-risk"> value-at-risk</a> </p> <a href="https://publications.waset.org/abstracts/115727/copula-markov-switching-multifractal-models-for-forecasting-value-at-risk" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115727.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">165</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1293</span> X̄ and S Control Charts based on Weighted Standard Deviation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Derya%20Karag%C3%B6z">Derya Karagöz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Shewhart chart based on normality assumption is not appropriate for skewed distributions since its Type-I error rate is inflated. This study presents X̄ and S control charts for monitoring the process variability for skewed distributions. We propose Weighted Standard Deviation (WSD) X̄ and S control charts. Standard deviation estimator is applied to monitor the process variability for estimating the process standard deviation, in the case of the W SD X̄ and S control charts as this estimator is simple and easy to compute. Unlike the Shewhart control chart, the proposed charts provide asymmetric limits in accordance with the direction and degree of skewness to construct the upper and lower limits. The performances of the proposed charts are compared with other heuristic charts for skewed distributions by using Simulation study. The Simulation studies show that the proposed control charts have good properties for skewed distributions and large sample sizes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=weighted%20standard%20deviation" title="weighted standard deviation">weighted standard deviation</a>, <a href="https://publications.waset.org/abstracts/search?q=MAD" title=" MAD"> MAD</a>, <a href="https://publications.waset.org/abstracts/search?q=skewed%20distributions" title=" skewed distributions"> skewed distributions</a>, <a href="https://publications.waset.org/abstracts/search?q=S%20control%20charts" title=" S control charts"> S control charts</a> </p> <a href="https://publications.waset.org/abstracts/45730/x-and-s-control-charts-based-on-weighted-standard-deviation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45730.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">399</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1292</span> Characterization of Probability Distributions through Conditional Expectation of Pair of Generalized Order Statistics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zubdahe%20Noor">Zubdahe Noor</a>, <a href="https://publications.waset.org/abstracts/search?q=Haseeb%20Athar"> Haseeb Athar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20order%20statistics" title="generalized order statistics">generalized order statistics</a>, <a href="https://publications.waset.org/abstracts/search?q=order%20statistics" title=" order statistics"> order statistics</a>, <a href="https://publications.waset.org/abstracts/search?q=record%20values" title=" record values"> record values</a>, <a href="https://publications.waset.org/abstracts/search?q=conditional%20expectation" title=" conditional expectation"> conditional expectation</a>, <a href="https://publications.waset.org/abstracts/search?q=characterization" title=" characterization"> characterization</a> </p> <a href="https://publications.waset.org/abstracts/22898/characterization-of-probability-distributions-through-conditional-expectation-of-pair-of-generalized-order-statistics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22898.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">460</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1291</span> Classification on Statistical Distributions of a Complex N-Body System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=David%20C.%20Ni">David C. Ni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Contemporary models for N-body systems are based on temporal, two-body, and mass point representation of Newtonian mechanics. Other mainstream models include 2D and 3D Ising models based on local neighborhood the lattice structures. In Quantum mechanics, the theories of collective modes are for superconductivity and for the long-range quantum entanglement. However, these models are still mainly for the specific phenomena with a set of designated parameters. We are therefore motivated to develop a new construction directly from the complex-variable N-body systems based on the extended Blaschke functions (EBF), which represent a non-temporal and nonlinear extension of Lorentz transformation on the complex plane – the normalized momentum spaces. A point on the complex plane represents a normalized state of particle momentums observed from a reference frame in the theory of special relativity. There are only two key parameters, normalized momentum and nonlinearity for modelling. An algorithm similar to Jenkins-Traub method is adopted for solving EBF iteratively. Through iteration, the solution sets show a form of σ + i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various distributions, such as 1-peak, 2-peak, and 3-peak etc. distributions and some of them are analog to the canonical distributions. The results of the numerical analysis demonstrate continuum-to-discreteness transitions, evolutional invariance of distributions, phase transitions with conjugate symmetry, etc., which manifest the construction as a potential candidate for the unification of statistics. We hereby classify the observed distributions on the finite convergent domains. Continuous and discrete distributions both exist and are predictable for given partitions in different regions of parameter-pair. We further compare these distributions with canonical distributions and address the impacts on the existing applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=blaschke" title="blaschke">blaschke</a>, <a href="https://publications.waset.org/abstracts/search?q=lorentz%20transformation" title=" lorentz transformation"> lorentz transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=complex%20variables" title=" complex variables"> complex variables</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous" title=" continuous"> continuous</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete" title=" discrete"> discrete</a>, <a href="https://publications.waset.org/abstracts/search?q=canonical" title=" canonical"> canonical</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a> </p> <a href="https://publications.waset.org/abstracts/51005/classification-on-statistical-distributions-of-a-complex-n-body-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51005.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">309</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1290</span> An AK-Chart for the Non-Normal Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chia-Hau%20Liu">Chia-Hau Liu</a>, <a href="https://publications.waset.org/abstracts/search?q=Tai-Yue%20Wang"> Tai-Yue Wang </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Traditional multivariate control charts assume that measurement from manufacturing processes follows a multivariate normal distribution. However, this assumption may not hold or may be difficult to verify because not all the measurement from manufacturing processes are normal distributed in practice. This study develops a new multivariate control chart for monitoring the processes with non-normal data. We propose a mechanism based on integrating the one-class classification method and the adaptive technique. The adaptive technique is used to improve the sensitivity to small shift on one-class classification in statistical process control. In addition, this design provides an easy way to allocate the value of type I error so it is easier to be implemented. Finally, the simulation study and the real data from industry are used to demonstrate the effectiveness of the propose control charts. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multivariate%20control%20chart" title="multivariate control chart">multivariate control chart</a>, <a href="https://publications.waset.org/abstracts/search?q=statistical%20process%20control" title=" statistical process control"> statistical process control</a>, <a href="https://publications.waset.org/abstracts/search?q=one-class%20classification%20method" title=" one-class classification method"> one-class classification method</a>, <a href="https://publications.waset.org/abstracts/search?q=non-normal%20data" title=" non-normal data"> non-normal data</a> </p> <a href="https://publications.waset.org/abstracts/7485/an-ak-chart-for-the-non-normal-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7485.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">422</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1289</span> Multivariate Analysis of Spectroscopic Data for Agriculture Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asmaa%20M.%20Hussein">Asmaa M. Hussein</a>, <a href="https://publications.waset.org/abstracts/search?q=Amr%20Wassal"> Amr Wassal</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Farouk%20Al-Sadek"> Ahmed Farouk Al-Sadek</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20F.%20Abd%20El-Rahman"> A. F. Abd El-Rahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, a multivariate analysis of potato spectroscopic data was presented to detect the presence of brown rot disease or not. Near-Infrared (NIR) spectroscopy (1,350-2,500 nm) combined with multivariate analysis was used as a rapid, non-destructive technique for the detection of brown rot disease in potatoes. Spectral measurements were performed in 565 samples, which were chosen randomly at the infection place in the potato slice. In this study, 254 infected and 311 uninfected (brown rot-free) samples were analyzed using different advanced statistical analysis techniques. The discrimination performance of different multivariate analysis techniques, including classification, pre-processing, and dimension reduction, were compared. Applying a random forest algorithm classifier with different pre-processing techniques to raw spectra had the best performance as the total classification accuracy of 98.7% was achieved in discriminating infected potatoes from control. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brown%20rot%20disease" title="Brown rot disease">Brown rot disease</a>, <a href="https://publications.waset.org/abstracts/search?q=NIR%20spectroscopy" title=" NIR spectroscopy"> NIR spectroscopy</a>, <a href="https://publications.waset.org/abstracts/search?q=potato" title=" potato"> potato</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20forest" title=" random forest"> random forest</a> </p> <a href="https://publications.waset.org/abstracts/127918/multivariate-analysis-of-spectroscopic-data-for-agriculture-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127918.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">190</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1288</span> Forecasting for Financial Stock Returns Using a Quantile Function Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuzhi%20Cai">Yuzhi Cai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduce a newly developed quantile function model that can be used for estimating conditional distributions of financial returns and for obtaining multi-step ahead out-of-sample predictive distributions of financial returns. Since we forecast the whole conditional distributions, any predictive quantity of interest about the future financial returns can be obtained simply as a by-product of the method. We also show an application of the model to the daily closing prices of Dow Jones Industrial Average (DJIA) series over the period from 2 January 2004 - 8 October 2010. We obtained the predictive distributions up to 15 days ahead for the DJIA returns, which were further compared with the actually observed returns and those predicted from an AR-GARCH model. The results show that the new model can capture the main features of financial returns and provide a better fitted model together with improved mean forecasts compared with conventional methods. We hope this talk will help audience to see that this new model has the potential to be very useful in practice. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=DJIA" title="DJIA">DJIA</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20returns" title=" financial returns"> financial returns</a>, <a href="https://publications.waset.org/abstracts/search?q=predictive%20distribution" title=" predictive distribution"> predictive distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=quantile%20function%20model" title=" quantile function model"> quantile function model</a> </p> <a href="https://publications.waset.org/abstracts/33434/forecasting-for-financial-stock-returns-using-a-quantile-function-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33434.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">367</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1287</span> The Moment of the Optimal Average Length of the Multivariate Exponentially Weighted Moving Average Control Chart for Equally Correlated Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edokpa%20Idemudia%20Waziri">Edokpa Idemudia Waziri</a>, <a href="https://publications.waset.org/abstracts/search?q=Salisu%20S.%20Umar"> Salisu S. Umar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Hotellng’s T^2 is a well-known statistic for detecting a shift in the mean vector of a multivariate normal distribution. Control charts based on T have been widely used in statistical process control for monitoring a multivariate process. Although it is a powerful tool, the T statistic is deficient when the shift to be detected in the mean vector of a multivariate process is small and consistent. The Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is one of the control statistics used to overcome the drawback of the Hotellng’s T statistic. In this paper, the probability distribution of the Average Run Length (ARL) of the MEWMA control chart when the quality characteristics exhibit substantial cross correlation and when the process is in-control and out-of-control was derived using the Markov Chain algorithm. The derivation of the probability functions and the moments of the run length distribution were also obtained and they were consistent with some existing results for the in-control and out-of-control situation. By simulation process, the procedure identified a class of ARL for the MEWMA control when the process is in-control and out-of-control. From our study, it was observed that the MEWMA scheme is quite adequate for detecting a small shift and a good way to improve the quality of goods and services in a multivariate situation. It was also observed that as the in-control average run length ARL0¬ or the number of variables (p) increases, the optimum value of the ARL0pt increases asymptotically and as the magnitude of the shift σ increases, the optimal ARLopt decreases. Finally, we use the example from the literature to illustrate our method and demonstrate its efficiency. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=average%20run%20length" title="average run length">average run length</a>, <a href="https://publications.waset.org/abstracts/search?q=markov%20chain" title=" markov chain"> markov chain</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20exponentially%20weighted%20moving%20average" title=" multivariate exponentially weighted moving average"> multivariate exponentially weighted moving average</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20smoothing%20parameter" title=" optimal smoothing parameter"> optimal smoothing parameter</a> </p> <a href="https://publications.waset.org/abstracts/42648/the-moment-of-the-optimal-average-length-of-the-multivariate-exponentially-weighted-moving-average-control-chart-for-equally-correlated-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42648.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">422</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1286</span> Parametric Inference of Elliptical and Archimedean Family of Copulas</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alam%20Ali">Alam Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Ashok%20Kumar%20Pathak"> Ashok Kumar Pathak</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nowadays, copulas have attracted significant attention for modeling multivariate observations, and the foremost feature of copula functions is that they give us the liberty to study the univariate marginal distributions and their joint behavior separately. The copula parameter apprehends the intrinsic dependence among the marginal variables, and it can be estimated using parametric, semiparametric, or nonparametric techniques. This work aims to compare the coverage rates between an Elliptical and an Archimedean family of copulas via a fully parametric estimation technique. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elliptical%20copula" title="elliptical copula">elliptical copula</a>, <a href="https://publications.waset.org/abstracts/search?q=archimedean%20copula" title=" archimedean copula"> archimedean copula</a>, <a href="https://publications.waset.org/abstracts/search?q=estimation" title=" estimation"> estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=coverage%20rate" title=" coverage rate"> coverage rate</a> </p> <a href="https://publications.waset.org/abstracts/171985/parametric-inference-of-elliptical-and-archimedean-family-of-copulas" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171985.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">66</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1285</span> A Bayesian Multivariate Microeconometric Model for Estimation of Price Elasticity of Demand</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jefferson%20Hernandez">Jefferson Hernandez</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20Padilla"> Juan Padilla</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Estimation of price elasticity of demand is a valuable tool for the task of price settling. Given its relevance, it is an active field for microeconomic and statistical research. Price elasticity in the industry of oil and gas, in particular for fuels sold in gas stations, has shown to be a challenging topic given the market and state restrictions, and underlying correlations structures between the types of fuels sold by the same gas station. This paper explores the Lotka-Volterra model for the problem for price elasticity estimation in the context of fuels; in addition, it is introduced multivariate random effects with the purpose of dealing with errors, e.g., measurement or missing data errors. In order to model the underlying correlation structures, the Inverse-Wishart, Hierarchical Half-t and LKJ distributions are studied. Here, the Bayesian paradigm through Markov Chain Monte Carlo (MCMC) algorithms for model estimation is considered. Simulation studies covering a wide range of situations were performed in order to evaluate parameter recovery for the proposed models and algorithms. Results revealed that the proposed algorithms recovered quite well all model parameters. Also, a real data set analysis was performed in order to illustrate the proposed approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=price%20elasticity" title="price elasticity">price elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=volume" title=" volume"> volume</a>, <a href="https://publications.waset.org/abstracts/search?q=correlation%20structures" title=" correlation structures"> correlation structures</a>, <a href="https://publications.waset.org/abstracts/search?q=Bayesian%20models" title=" Bayesian models"> Bayesian models</a> </p> <a href="https://publications.waset.org/abstracts/122666/a-bayesian-multivariate-microeconometric-model-for-estimation-of-price-elasticity-of-demand" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/122666.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">165</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1284</span> First Order Moment Bounds on DMRL and IMRL Classes of Life Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debasis%20Sengupta">Debasis Sengupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Das"> Sudipta Das</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The class of life distributions with decreasing mean residual life (DMRL) is well known in the field of reliability modeling. It contains the IFR class of distributions and is contained in the NBUE class of distributions. While upper and lower bounds of the reliability distribution function of aging classes such as IFR, IFRA, NBU, NBUE, and HNBUE have discussed in the literature for a long time, there is no analogous result available for the DMRL class. We obtain the upper and lower bounds for the reliability function of the DMRL class in terms of first order finite moment. The lower bound is obtained by showing that for any fixed time, the minimization of the reliability function over the class of all DMRL distributions with a fixed mean is equivalent to its minimization over a smaller class of distribution with a special form. Optimization over this restricted set can be made algebraically. Likewise, the maximization of the reliability function over the class of all DMRL distributions with a fixed mean turns out to be a parametric optimization problem over the class of DMRL distributions of a special form. The constructive proofs also establish that both the upper and lower bounds are sharp. Further, the DMRL upper bound coincides with the HNBUE upper bound and the lower bound coincides with the IFR lower bound. We also prove that a pair of sharp upper and lower bounds for the reliability function when the distribution is increasing mean residual life (IMRL) with a fixed mean. This result is proved in a similar way. These inequalities fill a long-standing void in the literature of the life distribution modeling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=DMRL" title="DMRL">DMRL</a>, <a href="https://publications.waset.org/abstracts/search?q=IMRL" title=" IMRL"> IMRL</a>, <a href="https://publications.waset.org/abstracts/search?q=reliability%20bounds" title=" reliability bounds"> reliability bounds</a>, <a href="https://publications.waset.org/abstracts/search?q=hazard%20functions" title=" hazard functions"> hazard functions</a> </p> <a href="https://publications.waset.org/abstracts/47988/first-order-moment-bounds-on-dmrl-and-imrl-classes-of-life-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47988.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1283</span> A Cohort and Empirical Based Multivariate Mortality Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jeffrey%20Tzu-Hao%20Tsai">Jeffrey Tzu-Hao Tsai</a>, <a href="https://publications.waset.org/abstracts/search?q=Yi-Shan%20Wong"> Yi-Shan Wong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This article proposes a cohort-age-period (CAP) model to characterize multi-population mortality processes using cohort, age, and period variables. Distinct from the factor-based Lee-Carter-type decomposition mortality model, this approach is empirically based and includes the age, period, and cohort variables into the equation system. The model not only provides a fruitful intuition for explaining multivariate mortality change rates but also has a better performance in forecasting future patterns. Using the US and the UK mortality data and performing ten-year out-of-sample tests, our approach shows smaller mean square errors in both countries compared to the models in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=longevity%20risk" title="longevity risk">longevity risk</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20mortality%20model" title=" stochastic mortality model"> stochastic mortality model</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20mortality%20rate" title=" multivariate mortality rate"> multivariate mortality rate</a>, <a href="https://publications.waset.org/abstracts/search?q=risk%20management" title=" risk management"> risk management</a> </p> <a href="https://publications.waset.org/abstracts/182234/a-cohort-and-empirical-based-multivariate-mortality-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182234.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">54</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1282</span> Introduction of Robust Multivariate Process Capability Indices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Behrooz%20Khalilloo">Behrooz Khalilloo</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamid%20Shahriari"> Hamid Shahriari</a>, <a href="https://publications.waset.org/abstracts/search?q=Emad%20Roghanian"> Emad Roghanian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Process capability indices (PCIs) are important concepts of statistical quality control and measure the capability of processes and how much processes are meeting certain specifications. An important issue in statistical quality control is parameter estimation. Under the assumption of multivariate normality, the distribution parameters, mean vector and variance-covariance matrix must be estimated, when they are unknown. Classic estimation methods like method of moment estimation (MME) or maximum likelihood estimation (MLE) makes good estimation of the population parameters when data are not contaminated. But when outliers exist in the data, MME and MLE make weak estimators of the population parameters. So we need some estimators which have good estimation in the presence of outliers. In this work robust M-estimators for estimating these parameters are used and based on robust parameter estimators, robust process capability indices are introduced. The performances of these robust estimators in the presence of outliers and their effects on process capability indices are evaluated by real and simulated multivariate data. The results indicate that the proposed robust capability indices perform much better than the existing process capability indices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multivariate%20process%20capability%20indices" title="multivariate process capability indices">multivariate process capability indices</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20M-estimator" title=" robust M-estimator"> robust M-estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=outlier" title=" outlier"> outlier</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20quality%20control" title=" multivariate quality control"> multivariate quality control</a>, <a href="https://publications.waset.org/abstracts/search?q=statistical%20quality%20control" title=" statistical quality control"> statistical quality control</a> </p> <a href="https://publications.waset.org/abstracts/81586/introduction-of-robust-multivariate-process-capability-indices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81586.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1281</span> Determining Best Fitting Distributions for Minimum Flows of Streams in Gediz Basin</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Naci%20B%C3%BCy%C3%BCkkarac%C4%B1%C4%9Fan">Naci Büyükkaracığan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Today, the need for water sources is swiftly increasing due to population growth. At the same time, it is known that some regions will face with shortage of water and drought because of the global warming and climate change. In this context, evaluation and analysis of hydrological data such as the observed trends, drought and flood prediction of short term flow has great deal of importance. The most accurate selection probability distribution is important to describe the low flow statistics for the studies related to drought analysis. As in many basins In Turkey, Gediz River basin will be affected enough by the drought and will decrease the amount of used water. The aim of this study is to derive appropriate probability distributions for frequency analysis of annual minimum flows at 6 gauging stations of the Gediz Basin. After applying 10 different probability distributions, six different parameter estimation methods and 3 fitness test, the Pearson 3 distribution and general extreme values distributions were found to give optimal results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gediz%20Basin" title="Gediz Basin">Gediz Basin</a>, <a href="https://publications.waset.org/abstracts/search?q=goodness-of-fit%20tests" title=" goodness-of-fit tests"> goodness-of-fit tests</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20flows" title=" minimum flows"> minimum flows</a>, <a href="https://publications.waset.org/abstracts/search?q=probability%20distribution" title=" probability distribution"> probability distribution</a> </p> <a href="https://publications.waset.org/abstracts/9078/determining-best-fitting-distributions-for-minimum-flows-of-streams-in-gediz-basin" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9078.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">271</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1280</span> A Non-parametric Clustering Approach for Multivariate Geostatistical Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francky%20Fouedjio">Francky Fouedjio</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multivariate geostatistical data have become omnipresent in the geosciences and pose substantial analysis challenges. One of them is the grouping of data locations into spatially contiguous clusters so that data locations within the same cluster are more similar while clusters are different from each other, in some sense. Spatially contiguous clusters can significantly improve the interpretation that turns the resulting clusters into meaningful geographical subregions. In this paper, we develop an agglomerative hierarchical clustering approach that takes into account the spatial dependency between observations. It relies on a dissimilarity matrix built from a non-parametric kernel estimator of the spatial dependence structure of data. It integrates existing methods to find the optimal cluster number and to evaluate the contribution of variables to the clustering. The capability of the proposed approach to provide spatially compact, connected and meaningful clusters is assessed using bivariate synthetic dataset and multivariate geochemical dataset. The proposed clustering method gives satisfactory results compared to other similar geostatistical clustering methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=clustering" title="clustering">clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=geostatistics" title=" geostatistics"> geostatistics</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20data" title=" multivariate data"> multivariate data</a>, <a href="https://publications.waset.org/abstracts/search?q=non-parametric" title=" non-parametric"> non-parametric</a> </p> <a href="https://publications.waset.org/abstracts/46870/a-non-parametric-clustering-approach-for-multivariate-geostatistical-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46870.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">477</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1279</span> On the Bootstrap P-Value Method in Identifying out of Control Signals in Multivariate Control Chart</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=O.%20Ikpotokin">O. Ikpotokin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In any production process, every product is aimed to attain a certain standard, but the presence of assignable cause of variability affects our process, thereby leading to low quality of product. The ability to identify and remove this type of variability reduces its overall effect, thereby improving the quality of the product. In case of a univariate control chart signal, it is easy to detect the problem and give a solution since it is related to a single quality characteristic. However, the problems involved in the use of multivariate control chart are the violation of multivariate normal assumption and the difficulty in identifying the quality characteristic(s) that resulted in the out of control signals. The purpose of this paper is to examine the use of non-parametric control chart (the bootstrap approach) for obtaining control limit to overcome the problem of multivariate distributional assumption and the p-value method for detecting out of control signals. Results from a performance study show that the proposed bootstrap method enables the setting of control limit that can enhance the detection of out of control signals when compared, while the p-value method also enhanced in identifying out of control variables. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bootstrap%20control%20limit" title="bootstrap control limit">bootstrap control limit</a>, <a href="https://publications.waset.org/abstracts/search?q=p-value%20method" title=" p-value method"> p-value method</a>, <a href="https://publications.waset.org/abstracts/search?q=out-of-control%20signals" title=" out-of-control signals"> out-of-control signals</a>, <a href="https://publications.waset.org/abstracts/search?q=p-value" title=" p-value"> p-value</a>, <a href="https://publications.waset.org/abstracts/search?q=quality%20characteristics" title=" quality characteristics"> quality characteristics</a> </p> <a href="https://publications.waset.org/abstracts/77853/on-the-bootstrap-p-value-method-in-identifying-out-of-control-signals-in-multivariate-control-chart" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77853.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">347</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1278</span> The Use of Boosted Multivariate Trees in Medical Decision-Making for Repeated Measurements</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ebru%20Turgal">Ebru Turgal</a>, <a href="https://publications.waset.org/abstracts/search?q=Beyza%20Doganay%20Erdogan"> Beyza Doganay Erdogan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Machine learning aims to model the relationship between the response and features. Medical decision-making researchers would like to make decisions about patients’ course and treatment, by examining the repeated measurements over time. Boosting approach is now being used in machine learning area for these aims as an influential tool. The aim of this study is to show the usage of multivariate tree boosting in this field. The main reason for utilizing this approach in the field of decision-making is the ease solutions of complex relationships. To show how multivariate tree boosting method can be used to identify important features and feature-time interaction, we used the data, which was collected retrospectively from Ankara University Chest Diseases Department records. Dataset includes repeated PF ratio measurements. The follow-up time is planned for 120 hours. A set of different models is tested. In conclusion, main idea of classification with weighed combination of classifiers is a reliable method which was shown with simulations several times. Furthermore, time varying variables will be taken into consideration within this concept and it could be possible to make accurate decisions about regression and survival problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boosted%20multivariate%20trees" title="boosted multivariate trees">boosted multivariate trees</a>, <a href="https://publications.waset.org/abstracts/search?q=longitudinal%20data" title=" longitudinal data"> longitudinal data</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20regression%20tree" title=" multivariate regression tree"> multivariate regression tree</a>, <a href="https://publications.waset.org/abstracts/search?q=panel%20data" title=" panel data"> panel data</a> </p> <a href="https://publications.waset.org/abstracts/87009/the-use-of-boosted-multivariate-trees-in-medical-decision-making-for-repeated-measurements" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87009.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">203</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1277</span> Analyzing the Influence of Hydrometeorlogical Extremes, Geological Setting, and Social Demographic on Public Health</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Irfan%20Ahmad%20Afip">Irfan Ahmad Afip</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This main research objective is to accurately identify the possibility for a Leptospirosis outbreak severity of a certain area based on its input features into a multivariate regression model. The research question is the possibility of an outbreak in a specific area being influenced by this feature, such as social demographics and hydrometeorological extremes. If the occurrence of an outbreak is being subjected to these features, then the epidemic severity for an area will be different depending on its environmental setting because the features will influence the possibility and severity of an outbreak. Specifically, this research objective was three-fold, namely: (a) to identify the relevant multivariate features and visualize the patterns data, (b) to develop a multivariate regression model based from the selected features and determine the possibility for Leptospirosis outbreak in an area, and (c) to compare the predictive ability of multivariate regression model and machine learning algorithms. Several secondary data features were collected locations in the state of Negeri Sembilan, Malaysia, based on the possibility it would be relevant to determine the outbreak severity in the area. The relevant features then will become an input in a multivariate regression model; a linear regression model is a simple and quick solution for creating prognostic capabilities. A multivariate regression model has proven more precise prognostic capabilities than univariate models. The expected outcome from this research is to establish a correlation between the features of social demographic and hydrometeorological with Leptospirosis bacteria; it will also become a contributor for understanding the underlying relationship between the pathogen and the ecosystem. The relationship established can be beneficial for the health department or urban planner to inspect and prepare for future outcomes in event detection and system health monitoring. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=geographical%20information%20system" title="geographical information system">geographical information system</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrometeorological" title=" hydrometeorological"> hydrometeorological</a>, <a href="https://publications.waset.org/abstracts/search?q=leptospirosis" title=" leptospirosis"> leptospirosis</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20regression" title=" multivariate regression"> multivariate regression</a> </p> <a href="https://publications.waset.org/abstracts/121967/analyzing-the-influence-of-hydrometeorlogical-extremes-geological-setting-and-social-demographic-on-public-health" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">115</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1276</span> Frequency Analysis Using Multiple Parameter Probability Distributions for Rainfall to Determine Suitable Probability Distribution in Pakistan</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tasir%20Khan">Tasir Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Yejuan%20Wang"> Yejuan Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study of extreme rainfall events is very important for flood management in river basins and the design of water conservancy infrastructure. Evaluation of quantiles of annual maximum rainfall (AMRF) is required in different environmental fields, agriculture operations, renewable energy sources, climatology, and the design of different structures. Therefore, the annual maximum rainfall (AMRF) was performed at different stations in Pakistan. Multiple probability distributions, log normal (LN), generalized extreme value (GEV), Gumbel (max), and Pearson type3 (P3) were used to find out the most appropriate distributions in different stations. The L moments method was used to evaluate the distribution parameters. Anderson darling test, Kolmogorov- Smirnov test, and chi-square test showed that two distributions, namely GUM (max) and LN, were the best appropriate distributions. The quantile estimate of a multi-parameter PD offers extreme rainfall through a specific location and is therefore important for decision-makers and planners who design and construct different structures. This result provides an indication of these multi-parameter distribution consequences for the study of sites and peak flow prediction and the design of hydrological maps. Therefore, this discovery can support hydraulic structure and flood management. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=RAMSE" title="RAMSE">RAMSE</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20frequency%20analysis" title=" multiple frequency analysis"> multiple frequency analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=annual%20maximum%20rainfall" title=" annual maximum rainfall"> annual maximum rainfall</a>, <a href="https://publications.waset.org/abstracts/search?q=L-moments" title=" L-moments"> L-moments</a> </p> <a href="https://publications.waset.org/abstracts/161973/frequency-analysis-using-multiple-parameter-probability-distributions-for-rainfall-to-determine-suitable-probability-distribution-in-pakistan" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161973.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">81</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1275</span> Classification of Generative Adversarial Network Generated Multivariate Time Series Data Featuring Transformer-Based Deep Learning Architecture</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Thrivikraman%20Aswathi">Thrivikraman Aswathi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Advaith"> S. Advaith</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As there can be cases where the use of real data is somehow limited, such as when it is hard to get access to a large volume of real data, we need to go for synthetic data generation. This produces high-quality synthetic data while maintaining the statistical properties of a specific dataset. In the present work, a generative adversarial network (GAN) is trained to produce multivariate time series (MTS) data since the MTS is now being gathered more often in various real-world systems. Furthermore, the GAN-generated MTS data is fed into a transformer-based deep learning architecture that carries out the data categorization into predefined classes. Further, the model is evaluated across various distinct domains by generating corresponding MTS data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=GAN" title="GAN">GAN</a>, <a href="https://publications.waset.org/abstracts/search?q=transformer" title=" transformer"> transformer</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20time%20series" title=" multivariate time series"> multivariate time series</a> </p> <a href="https://publications.waset.org/abstracts/157460/classification-of-generative-adversarial-network-generated-multivariate-time-series-data-featuring-transformer-based-deep-learning-architecture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157460.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">130</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1274</span> Schrödinger Equation with Position-Dependent Mass: Staggered Mass Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20J.%20Pe%C3%B1a">J. J. Peña</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Morales"> J. Morales</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Garc%C3%ADa-Ravelo"> J. García-Ravelo</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Arcos-D%C3%ADaz"> L. Arcos-Díaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=free%20particle" title="free particle">free particle</a>, <a href="https://publications.waset.org/abstracts/search?q=point%20canonical%20transformation%20method" title=" point canonical transformation method"> point canonical transformation method</a>, <a href="https://publications.waset.org/abstracts/search?q=position-dependent%20mass" title=" position-dependent mass"> position-dependent mass</a>, <a href="https://publications.waset.org/abstracts/search?q=staggered%20mass%20distribution" title=" staggered mass distribution"> staggered mass distribution</a> </p> <a href="https://publications.waset.org/abstracts/71082/schrodinger-equation-with-position-dependent-mass-staggered-mass-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71082.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">403</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1273</span> An Application of Modified M-out-of-N Bootstrap Method to Heavy-Tailed Distributions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hannah%20F.%20Opayinka">Hannah F. Opayinka</a>, <a href="https://publications.waset.org/abstracts/search?q=Adedayo%20A.%20Adepoju"> Adedayo A. Adepoju </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study is an extension of a prior study on the modification of the existing m-out-of-n (moon) bootstrap method for heavy-tailed distributions in which modified m-out-of-n (mmoon) was proposed as an alternative method to the existing moon technique. In this study, both moon and mmoon techniques were applied to two real income datasets which followed Lognormal and Pareto distributions respectively with finite variances. The performances of these two techniques were compared using Standard Error (SE) and Root Mean Square Error (RMSE). The findings showed that mmoon outperformed moon bootstrap in terms of smaller SEs and RMSEs for all the sample sizes considered in the two datasets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bootstrap" title="Bootstrap">Bootstrap</a>, <a href="https://publications.waset.org/abstracts/search?q=income%20data" title=" income data"> income data</a>, <a href="https://publications.waset.org/abstracts/search?q=lognormal%20distribution" title=" lognormal distribution"> lognormal distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=Pareto%20distribution" title=" Pareto distribution"> Pareto distribution</a> </p> <a href="https://publications.waset.org/abstracts/104327/an-application-of-modified-m-out-of-n-bootstrap-method-to-heavy-tailed-distributions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/104327.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">186</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1272</span> Multi-scale Spatial and Unified Temporal Feature-fusion Network for Multivariate Time Series Anomaly Detection</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hang%20Yang">Hang Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jichao%20Li"> Jichao Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Kewei%20Yang"> Kewei Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Tianyang%20Lei"> Tianyang Lei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multivariate time series anomaly detection is a significant research topic in the field of data mining, encompassing a wide range of applications across various industrial sectors such as traffic roads, financial logistics, and corporate production. The inherent spatial dependencies and temporal characteristics present in multivariate time series introduce challenges to the anomaly detection task. Previous studies have typically been based on the assumption that all variables belong to the same spatial hierarchy, neglecting the multi-level spatial relationships. To address this challenge, this paper proposes a multi-scale spatial and unified temporal feature fusion network, denoted as MSUT-Net, for multivariate time series anomaly detection. The proposed model employs a multi-level modeling approach, incorporating both temporal and spatial modules. The spatial module is designed to capture the spatial characteristics of multivariate time series data, utilizing an adaptive graph structure learning model to identify the multi-level spatial relationships between data variables and their attributes. The temporal module consists of a unified temporal processing module, which is tasked with capturing the temporal features of multivariate time series. This module is capable of simultaneously identifying temporal dependencies among different variables. Extensive testing on multiple publicly available datasets confirms that MSUT-Net achieves superior performance on the majority of datasets. Our method is able to model and accurately detect systems data with multi-level spatial relationships from a spatial-temporal perspective, providing a novel perspective for anomaly detection analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=data%20mining" title="data mining">data mining</a>, <a href="https://publications.waset.org/abstracts/search?q=industrial%20system" title=" industrial system"> industrial system</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20time%20series" title=" multivariate time series"> multivariate time series</a>, <a href="https://publications.waset.org/abstracts/search?q=anomaly%20detection" title=" anomaly detection"> anomaly detection</a> </p> <a href="https://publications.waset.org/abstracts/193205/multi-scale-spatial-and-unified-temporal-feature-fusion-network-for-multivariate-time-series-anomaly-detection" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/193205.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">15</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1271</span> Evaluating Forecasts Through Stochastic Loss Order</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wilmer%20Osvaldo%20Martinez">Wilmer Osvaldo Martinez</a>, <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Dario%20Hernandez"> Manuel Dario Hernandez</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20Manuel%20Julio"> Juan Manuel Julio</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose to assess the performance of k forecast procedures by exploring the distributions of forecast errors and error losses. We argue that non systematic forecast errors minimize when their distributions are symmetric and unimodal, and that forecast accuracy should be assessed through stochastic loss order rather than expected loss order, which is the way it is customarily performed in previous work. Moreover, since forecast performance evaluation can be understood as a one way analysis of variance, we propose to explore loss distributions under two circumstances; when a strict (but unknown) joint stochastic order exists among the losses of all forecast alternatives, and when such order happens among subsets of alternative procedures. In spite of the fact that loss stochastic order is stronger than loss moment order, our proposals are at least as powerful as competing tests, and are robust to the correlation, autocorrelation and heteroskedasticity settings they consider. In addition, since our proposals do not require samples of the same size, their scope is also wider, and provided that they test the whole loss distribution instead of just loss moments, they can also be used to study forecast distributions as well. We illustrate the usefulness of our proposals by evaluating a set of real world forecasts. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=forecast%20evaluation" title="forecast evaluation">forecast evaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20order" title=" stochastic order"> stochastic order</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20comparison" title=" multiple comparison"> multiple comparison</a>, <a href="https://publications.waset.org/abstracts/search?q=non%20parametric%20test" title=" non parametric test"> non parametric test</a> </p> <a href="https://publications.waset.org/abstracts/167870/evaluating-forecasts-through-stochastic-loss-order" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167870.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">89</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multivariate%20distributions&page=6">6</a></li> 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