CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'managed',cRay: '91c6dd9c7d6b40f4',cH: 'clka0kSqkGjn4lFC8wn7vSr6Zl2jMOMN0DXrBmurymY-1741316668-1.2.1.1-LO9T707zqAes2b4I4Z0udwPufLVRMsgtsqoe9h49vnnWIGz55kJjHSd9zwWk2Izq',cUPMDTk: "\/abstracts\/search?q=fractile%20curves&__cf_chl_tk=e7m.QmOb8Aeeo7rbf7RadorZFYfJOnA7KNPoyNe0m1s-1741316668-1.0.1.1-RsAq0e5o3Epe7qV8tu08xqSGlgMcbj3INrxV9euFzZE",cFPWv: 'g',cITimeS: '1741316668',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=fractile%20curves&__cf_chl_f_tk=e7m.QmOb8Aeeo7rbf7RadorZFYfJOnA7KNPoyNe0m1s-1741316668-1.0.1.1-RsAq0e5o3Epe7qV8tu08xqSGlgMcbj3INrxV9euFzZE",md: "YNVnky6TxLB0UxDZdeudrjxsP75k_ZK64Y.i1Czoo4A-1741316668-1.2.1.1-AMm6VvjtrPmJoeUjgPKNvpMh5lcgVxxPPJR6CKFVviEiRbP08yriLBrSJ7cPU.NOs1_2sqe0i7j9ZTBquqgodkdaslaJV1IUkPiuGnBYH.FUvo34CbdkUQB9Uo.cAtZq9g_dxE3Vxv87_9gxoiYpJbqDS8qBHIuSyocbiGGbk2tEacKS2FvUu5AsN5mcByxWj4F9_XQWXWluBPavkCph8vILyKhY8K9_MQjXYt1grKr80ZzUQ_AsErCHJMtItAH__HvUEcqoseA.w67rCmw32Bw4tPBgAys9I2Ypfbo9DBEp5xOPTaif3vQRD6nX1mdYl4v_C.Vg36KsX_8OKMluNVvs7W4kwbrFyN9KqiAsnV9mD7pqmVov7FrNB35AOotHDzUluCjM5IGwy2Svz2TW5ul.eFSqTkfYdgeYTGLTKXXnyApn5E7Te5JXvq9Z57S_LbRbTIYa.E0HxCCmw0SuvgYJo9g_RL7Bgh3f.qIDcIKu03c9Ca5Qti92z2h50lBNAKpVw77vPBWyDBLuOpO5BkiM2qr3KOQFgLgePIKgnYyyrc4BMt98IqfY2AJBONQMWhSBCmOudM7EiUWB3hTh8.I6h1rTfZ2J_iNPLDU01Oq6ABHICdxIKtiHCiIuohbfR4rgaxJgc.HHFpgqKHddDaxBlS7S9OWIoxPLrLaVMhaTrKsP1MmHWQknxIXMU2Ku7Mvi3mFwq3wE5e.fJgcVW_zRciorsI7QL6kYw5ql1x8i.Nv3mImeEh1BqE1YHplLP34o1Tas5pP3Lk9L0TL7NHtZltmhecYy.11bE.BRTxhgJ96iEiPK72DzlCaD_DAgubaLV6sxkwdz1Vtnofn3cAEZdELdG.r0B9xXwQSRJe4o7wGr48HneyE2DJdiEWdf.reJ5XFgFxrFLKcJPlf.A_1M2Wmt0ZT3QboTd0gsMIwEFU5hyXCCB8I4rbMXDWk_54PC6N9iTDvOZAGsByCXq5GYI4E_EqjjyqpPeEOKqFjqYeOLgfv4N6q8MXkdWtROkZwuuX6vElzEWQy0pXlFC8Q97IkeRTksNowEBm81uxhCbWMVV5uIieTtxmZX0RGMHlCj1IHs6Xkiz5EGDTKz84zZtZUXZOYRalje9cA2z8Mn_K07.IgjALqJljuq614z.FLuik33e.PmGBaC3_sB9FBHyM.yDNOLnc2AwVGntT6GXFsFzOUEnhtnjgFo0Bpe9zqPC0wmIpY.2k1w55v.vZhj17Aj3vYVAEiLYIRDgkUZtCdFatzUOEgLqXQtfBRKoMexzF63UF8ZjpoBViVf7Q",mdrd: "WrIf.8CfCuzQ8b9M0yJPVdPFLlzACikwxdqbkfXN9oA-1741316668-1.2.1.1-gowyYECVszdk7jXl108Xp2E0FkAu38JCcdfvT_n85YetzGtrKcR4hTw_MouL_p_GSVW3RAIFNLLVA8gaZ93KV4sAmXfkRAd0_.ya4ate1pN1MmZxcjNcbHDCgrcDQQr1w4Wfv0f3AIyS7mx9OqxP_GJnvDXgUPH4pQjNf2VjNms0im3FPjP3.53QscDkcdPkoJT_DjtAsEUnE0o1aTWOZRtgNwJssp8HeADH8C5qcc8r1vf5CYXPG0Q0LwKWADjXNzpuK1lvP_5jlj5BVT8MDkQ3U0rGMZxk_rDoe5FNvtLgSQdL_Nt8RsSgqDTlrAKs4mARgdk4LJtrIa07haPZmo1UuODTfPp9yMZJf9QG30LJsXNgXKiWgQL9rNvIR4TkKJbNHNUAVBEtW0_E6FKrAZxqn4Iini4_gPP8c_ge432kYdMH46CKMdW_y9HtS4Budmt8x6LfO5r8fRNcLG1W27jGTdXgC0.of8qegKVqZ7.jqgcp5WLadtIqjQehIGLX2CGgafbUGjygbT0mEjdbE0OYsjU_g.fVOCCPq2G8.yXpglXilo4ZU2jaZduX2p5cKVXGGGjbyhuqezCV2m.ZF5.nwhYEdTMFUzBcHrb6SLhBP3ksEzwYSXUasSKCGpLpjDhJIYKyYVXj_p1zv7Spanc1Db02vKbxm72K8rWB5N1EzHEcKPMsnCehjs7RP7fYgFOsH_zXtoXCzXUMs5MR6ps_.dHtDGR3nAcIKcnLjIdqvHtQ.VgHdcaXlmsL0drSj5f8v7m1E1Hpfdh1ZUOzQy3DPbHS8GGj3qtZcQmZT1qv_zefXjtD.1i.QBDUTExDtx8SHLnME92BsBPvnxkyt5DtJ8YIVXDystyPx2D2Nu4oRbidtE2pjvmSSblRYItlxA66bP8X.6RDAKVXefAlhrC1wdPdSZrfry1mHcT843dicTbU5laM17KP.AMdwApUWauUpeuNB2HLJNqGuIxj6.ksaIeNOiWYYNht6M4OongAF64gYFTwvtMICtWZtmEF0Jd44Q_RSCsCZsD7Sfyn_hlrbeClJRyvoJWeRjLBehE7I9G6AiYU.l6LnUPAghPc7yiG1tEOK_jh.HGygvoElKo72dQgSCTgV5IyMZhroSWPXeuVaUhJQ.TTk7Tu6lKBf_57jORPpqQSvcQlmvXySp6NumSyvrGdWQpRKk_XQFJI1jKAspC.RAQLL2dE5adeZPdVxMdJjwkaklAo92Ggm1.dSHhboD.KH9XZGmyhOL25XsRLNkLBUV8f0Y9V7soRtdisVpr2tW4TYxGIYAOAd2H55poyT8MBf2uO.YKif4MWMTKNhe.7A73EpkeEhD84qQlb40Eu0fnEx.VhAI5U6TvCpyZPHyRQ0klH0ysLEETz_RsAgEr2VV6FOn8S_eJzcnkWMjXAx93Lnk41wDWcxUEr_g3tnRwY.pRr0Rvpbdous43POMteSnR5rrBdAldLMLjdemB2T4GpwHA5sYEDLZs5FrYH3bw3cIQiCf9HrEMd0qRa9rK4vB0iW_pJ_NcLUzyO4d5McGhv5ug9cl8n1GMACVjWZkpG_jjjBo8ssnJEazc85ai3_VUtUJrYO.x1uxlpWDGxI8veA7nseqagnbuJ9cL0WJHwjwDN7_4iBF.RPRmRki1XO1CIK.FBqSmLClEJIq4J1ZBnTGrbrYLGh1NviJvx8CddCYXCQ6bHIz5KFA9ch62zePCoKO4xr1c_xjfrrescclosPMTFrsRK6bQ17JSyEEXdZ2POOhmEyYV9AF0MRwCJN_ILSa7eAB87Ey6BVnFznU4RLzDCskSGlZiI7jTJJSrTYrcX1Zv6W8wPBiOKYZYPkmVGU1QGDLsOHgIhc74LIYN_DdXPYOTwtLH9BjPrh3Rmq33drOKX2V_0lQluG06sBrCXWWiHtaHIYdtjzeU6ylR5YtnutXj1xYKrCK7WqDAfyMmZklEubF7QNHn88h9vMLFsywuU.0sU3Rgxn32alYTNVHNdfa2LsQ"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/g/orchestrate/chl_page/v1?ray=91c6dd9c7d6b40f4';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=fractile%20curves&__cf_chl_rt_tk=e7m.QmOb8Aeeo7rbf7RadorZFYfJOnA7KNPoyNe0m1s-1741316668-1.0.1.1-RsAq0e5o3Epe7qV8tu08xqSGlgMcbj3INrxV9euFzZE" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>