IJPAM: Volume 77, No. 2 (2012)

FITTING PARETO DISTRIBUTION WITH
HYPEREXPONENTIAL TO EVALUATE
THE ARL FOR CUSUM CHART

Kanita Petcharat$^1$, Yupaporn Areepong$^{2}$,
Saowanit Sukparungsee$^3$, Gabriel Mititelu$^4$
$^{1,2,3}$Department of Applied Statistics
Faculty of Applied Science
King Mongkut's University of Technology
North Bangkok,Bangkok 10800, THAILAND
$^{4}$Department of Mathematical Sciences
University of Technology Sydney
Broadway, NSW 2007, AUSTRALIA


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.

Received: February 11, 2012

AMS Subject Classification: 60A05

Key Words and Phrases: cumulative sum chart, average run length, hyperexponential distribution, stopping times

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 2