Overlap coefficient (OVL) represents the proportion of overlap between two probability distributions, as a measure of the similarity between them. In this paper, we define a new overlap coefficient Λ based on Kullback-Leibler divergence and compare its performance to three known overlap coefficients, namely Matusia's Measure, Morisita's Measure, Weitzman's Measure. We study their properties, relations between them, and give approximate expressions for the biases and the variances.

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This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefcients, namely: Matusita's measure r, Morisita's measure l and Weitzman's measure D. A new overlap measure L based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefcients also are presented. Taylor series approximation is used to construct condence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

The choice of bandwidth is crucial to the kernel density estimation (KDE).Various bandwidth selection methods for KDE, least squares cross-validation (LSCV) and Kullback-Leibler cross-validation are proposed. We propose a method to select the optimal bandwidth for the KDE. The idea behind this method is to generalize the LSCV method, using the measure of ; divergence -β HAMZA DHAKER et al. 58 and to see the improvement in our method, we will compare these ( )bandwidth selector with a normal reference (NR), the last squares crossvalidation (LSCV), the Sheather and Jones (SJ) method, and the generalized ( )bandwidth selector, on simulated data. The use of the various practical bandwidth selectors is illustrated on a real data example.

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