Inference on overlap coefficients under the Weibull distribution : equal shape parameter
ESAIM: Probability and Statistics, Volume 9 (2005), pp. 206-219.

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.

DOI: 10.1051/ps:2005010
Classification: 62F10,  62F40
Keywords: bootstrap method, Matusia's measure, Morisita's measure, overlap coefficients, Taylor expansion, Weitzman's measure
     author = {Al-Saidy, Obaid and Samawi, Hani M. and Al-Saleh, Mohammad F.},
     title = {Inference on overlap coefficients under the {Weibull} distribution : equal shape parameter},
     journal = {ESAIM: Probability and Statistics},
     pages = {206--219},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2005},
     doi = {10.1051/ps:2005010},
     zbl = {1136.62378},
     mrnumber = {2148967},
     language = {en},
     url = {}
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Al-Saidy, Obaid; Samawi, Hani M.; Al-Saleh, Mohammad F. Inference on overlap coefficients under the Weibull distribution : equal shape parameter. ESAIM: Probability and Statistics, Volume 9 (2005), pp. 206-219. doi : 10.1051/ps:2005010.

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