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.

Nonparametric density estimation, based on kernel-type estimators, is a very popular method in statistical research, especially when we want to model the probabilistic or stochastic structure of a data set. In this paper, we investigate the asymptotic confidence bands for the distribution with kernel-estimators for some types of divergence measures (Rényi-α and Tsallis-α divergence). Our aim is to use the method based on empirical process techniques, in order to derive some asymptotic results. Under different assumptions, we establish a variety of fundamental and theoretical properties, such as the strong consistency of an uniform-in-bandwidth of the divergence estimators. We further apply the previous results in simulated examples, including the kernel-type estimator for Hellinger, Bhattacharyya and Kullback-Leibler divergence, to illustrate this approach, and we show that that the method performs competitively.

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.

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.

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