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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 andWeitzman's measure Δ. These measures are usually used inquantitative ecology and stress-strength models of reliabilityanalysis. Herein we consider two Weibull distributions havingthe same shape parameter and different scale parameters. Thisdistribution is known to be the most flexible life distributionmodel with two parameters. Monte Carlo evaluations are used tostudy the bias and precision of some estimators of these overlapmeasures. Confidence intervals for the measures are alsoconstructed via bootstrap methods and Taylor series approximation.

Keywords

Bootstrap methodMatusia's measureMorisita's measureOverlap coefficientsTaylor expansionWeitzman's measure.

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 206 - 219
Copyright
© EDP Sciences, SMAI, 2005

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