Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case

Version 1 : Received: 7 November 2018 / Approved: 8 November 2018 / Online: 8 November 2018 (10:07:22 CET)

How to cite: Dhaker, H.; Ngom, P.; Ibrahimou, B.; Mbodji, M. Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case. Preprints 2018, 2018110197 (doi: 10.20944/preprints201811.0197.v1). Dhaker, H.; Ngom, P.; Ibrahimou, B.; Mbodji, M. Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case. Preprints 2018, 2018110197 (doi: 10.20944/preprints201811.0197.v1).

## Abstract

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 KullbackLeibler divergence and compare its performance to three known overlap coefficients, namely Matusia’s Measure ρ, Morisita’s Measure λ, Weitzman’s Measure δ. We study their properties, relations between them, and give approximate expressions for the biases and the variances.

## Keywords

KullbackLeibler;OverlapCoefficients;NormalDensity.

## Subject

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

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