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ESAIM: Probability and Statistics ESAIM: Probability and Statistics

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Inference on overlap coefficients under the Weibull distribution: Equalshape parameter

Published online by Cambridge University Press:  15 November 2005

Obaid Al-Saidy ,
Hani M. Samawi  and
Mohammad F. Al-Saleh
Obaid Al-Saidy
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, P.C. 123 Al-Khod, Sultanate of Oman; obiad@squ.edu.om
Hani M. Samawi
Affiliation:
Department of Statistics, Yarmouk University, Irbid-Jordan 211-63, Jordan; hsamawi@yu.edu.jo; m-saleh@yu.edu.jo
Mohammad F. Al-Saleh
Affiliation:
Department of Statistics, Yarmouk University, Irbid-Jordan 211-63, Jordan; hsamawi@yu.edu.jo; m-saleh@yu.edu.jo
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Abstract

In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure Δ. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision of some estimators of these overlap measures. Confidence intervals for the measures are also constructed via bootstrap methods and Taylor series approximation.

Keywords

Bootstrap method Matusia's measure Morisita's measure Overlap coefficients Taylor expansion Weitzman's measure.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 206 - 219
Copyright
© EDP Sciences, SMAI, 2005

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