Estimation of Overlapping Measures using Numerical Approximations: Weibull Distributions

Abstract

This paper deals with the estimation problem of the two overlapping (OVL) measures, namely; Matusita ρ and Morisita λ measures when two independent random variables X and Y follow Weibull distribution. The two measures ρ and λ have been studied in the literature in the case of two Weibull distributions under the assumption that the two shape parameters are equal. In this work, a new general expression for each measure is provided under the Weibull distribution without using any assumptions about the distribution parameters. The numerical
integration methods known as trapezoidal, Simpson 1/3 and Simpson 3/8 rules that facilitate making inference on these measures are utilized. The relative bias (RB) and relative mean square error (RMSE) of the resulting proposed estimators were investigated and compared with some existing estimators via Monte-Carlo simulation technique. The results demonstrated clearly the superiority of the proposed estimators over the existing one in almost all considered cases.

Key words and phrases. Overlapping Measure, Maximum Likelihood Method, Numerical Integration Methods, Weibull Distribution, Relative bias, Relative mean square error.

2010 Mathematics Subject Classification. 62F10, 62F12