Fitting PARETO distribution with hyperexponential to evaluate the ARL for CUSUM chart

Kanita Petcharat; Yupaporn Areepong; Saowanit Sukparungsee; Gabriel Mititelu

Fitting PARETO distribution with hyperexponential to evaluate the ARL for CUSUM chart

Kanita Petcharat, Yupaporn Areepong, Saowanit Sukparungsee, Gabriel Mititelu

Western Sydney University

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Explicit formulas for the Average Run Length (ARL) of Cumulative Sum (CUSUM) chart are very complicated in regarding the analytical derivation when observations are Long-tailed distributions. The objective of this paper is to fitting Pareto distribution with the hyperexponential distribution to evaluate ARL of CUSUM procedure. The numerical results obtained from analytical solution for the ARL and from numerical approximations are derived and we compared the result with integral equations approach.

Original language	English
Pages (from-to)	233-244
Number of pages	12
Journal	International Journal of Pure and Applied Mathematics
Volume	77
Issue number	2
Publication status	Published - 2012

Keywords

CUSUM technique
integral equations
numerical integration

Cite this

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title = "Fitting PARETO distribution with hyperexponential to evaluate the ARL for CUSUM chart",

abstract = "Explicit formulas for the Average Run Length (ARL) of Cumulative Sum (CUSUM) chart are very complicated in regarding the analytical derivation when observations are Long-tailed distributions. The objective of this paper is to fitting Pareto distribution with the hyperexponential distribution to evaluate ARL of CUSUM procedure. The numerical results obtained from analytical solution for the ARL and from numerical approximations are derived and we compared the result with integral equations approach.",

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AU - Petcharat, Kanita

AU - Areepong, Yupaporn

AU - Sukparungsee, Saowanit

AU - Mititelu, Gabriel

PY - 2012

Y1 - 2012

N2 - Explicit formulas for the Average Run Length (ARL) of Cumulative Sum (CUSUM) chart are very complicated in regarding the analytical derivation when observations are Long-tailed distributions. The objective of this paper is to fitting Pareto distribution with the hyperexponential distribution to evaluate ARL of CUSUM procedure. The numerical results obtained from analytical solution for the ARL and from numerical approximations are derived and we compared the result with integral equations approach.

AB - Explicit formulas for the Average Run Length (ARL) of Cumulative Sum (CUSUM) chart are very complicated in regarding the analytical derivation when observations are Long-tailed distributions. The objective of this paper is to fitting Pareto distribution with the hyperexponential distribution to evaluate ARL of CUSUM procedure. The numerical results obtained from analytical solution for the ARL and from numerical approximations are derived and we compared the result with integral equations approach.

KW - CUSUM technique

KW - integral equations

KW - numerical integration

UR - https://hdl.handle.net/1959.7/uws:57780

UR - http://ijpam.eu/contents/2012-77-2/9/

M3 - Article

SN - 1311-8080

VL - 77

SP - 233

EP - 244

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

IS - 2

ER -

Fitting PARETO distribution with hyperexponential to evaluate the ARL for CUSUM chart

Abstract

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