In this paper we consider three measures of overlap, namely Matusia’s measure $\rho $, Morisita’s measure $\lambda $ and Weitzman’s measure $\Delta $. 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.

Classification : 62F10, 62F40

Mots clés : bootstrap method, Matusia's measure, Morisita's measure, overlap coefficients, Taylor expansion, Weitzman's measure

@article{PS_2005__9__206_0, 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 = {http://www.numdam.org/articles/10.1051/ps:2005010/} }

TY - JOUR AU - Al-Saidy, Obaid AU - Samawi, Hani M. AU - Al-Saleh, Mohammad F. TI - Inference on overlap coefficients under the Weibull distribution : equal shape parameter JO - ESAIM: Probability and Statistics PY - 2005 DA - 2005/// SP - 206 EP - 219 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2005010/ UR - https://zbmath.org/?q=an%3A1136.62378 UR - https://www.ams.org/mathscinet-getitem?mr=2148967 UR - https://doi.org/10.1051/ps:2005010 DO - 10.1051/ps:2005010 LA - en ID - PS_2005__9__206_0 ER -

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, Tome 9 (2005), pp. 206-219. doi : 10.1051/ps:2005010. http://www.numdam.org/articles/10.1051/ps:2005010/

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