Estimation of Pianka and Kullback-Leibler Overlapping Coefficients: Weibull Distributions

Abstract

This paper deals with the estimation problem of two the overlapping (OVL) coefficients known as Pianka`s (PI) and Kullback-Leibler`s (KL) measures when two independent random variables 𝑋 and 𝑌 follow Weibull distributions with the same shape parameters. The maximum likelihood estimator (MLE) procedures of the distributions parameters are considered and then the point and interval estimators of PI and KL are obtained. A limited simulation study is achieved to study the behavior of the interested point estimators for finite sample sizes.