ESAIM: Probability and Statistics (ESAIM: P&S)

ESAIM: P&S, June 2005, Vol. 9, pp. 206-219
DOI: 10.1051/ps:2005010

Inference on overlap coefficients under the Weibull distribution: Equal shape parameter

Obaid Al-Saidy¹, Hani M. Samawi² and Mohammad F. Al-Saleh²

¹ Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, P.C. 123 Al-Khod, Sultanate of Oman; obiad@squ.edu.om
² Department of Statistics, Yarmouk University, Irbid-Jordan 211-63, Jordan; hsamawi@yu.edu.jo; m-saleh@yu.edu.jo

(Received July 5, 2004.)

Abstract
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.

Mathematics Subject Classification. 62F10, 62F40

Key words: Bootstrap method, Matusia's measure, Morisita's measure, Overlap coefficients, Taylor expansion, Weitzman's measure.

© EDP Sciences, SMAI 2005