Numerical Integration Approximations to Estimate the Weitzman Overlapping Measure: Weibull Distributions

Abstract

This paper deals with the problem of estimating the overlapping (OVL) Weitzman measure (∆) when two independent random variables X and Y are given by twoparameter Weibull distribution. The measure ∆ has 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 general expression for the Weitzmans measure is provided under the Weibull distribution without using any assumptions about the distribution parameters. Some new estimators for ∆ are developed depending on three numerical integration rules known as trapezoidal, Simpson 1/3 and Simpson 3/8 rules. The performance of the proposed estimators were investigated and compared with some existing estimators via simulation technique and real data. The results demonstrated the superiority of the proposed estimators over the existing one in almost all considered cases.