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

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 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.

Cultural Differences in an Artificial Representation of the Human Emotional Brain System: A Deep Learning Study

“…Similarly, the fixation index measure from population biology has been proposed as a measure of cultural differences (Muthukrishna et al 2020). Most of these approaches maintain the simplifying assumption of normality (Messner and Schäfer 2015), although Messner (2021b) provides distribution-free algorithms using the Gini/Weitzmann overlapping index (Deutsch and Silber 1997; Gini 1916; Gini and Livada 1959; Weitzman 1970) and the Kullback–Leibler divergence criteria (Dhaker et al 2019; Kullback and Leibler 1951). Fifth, and continuing to work with individual-level data rather than country averages in order to consider both cultural heterogeneity within and overlaps between countries, Messner (2022a) deploys a Kohonen (2001) self-organizing map as an unsupervised machine learning algorithm to identify distinct worldwide cultural prototypes.…”

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

“…There are another OVL measures that studied in the literature, such as Matusita measure (𝜌), Morsita measure (𝜆) and Weitzman measure (∆) (see and Eidous and Al-Talafha, 2020). There are another two overlap coefficients (OVL) known as, Pianka`s measure (PI) (see Chauby et al, 2008) and Kullback-Leibler`s (KL) (see Dhaker et al, 2019 and2021). The various OVL measures have been used in ecology and stress-strength model of reliability analysis (Ichikawa1993).…”

“…There are another OVL measures that studied in the literature, such as Matusita measure (𝜌), Morsita measure (𝜆) and Weitzman measure (∆) (see and Al-Talafha, 2020 andAl-Daradkeh, 2022 and the references therein). The overlap measures are commonly used is reliability analysis to estimate the proportion of machine or electronic devices that have similar range of failure time (Dhaker et al,2019) and genetics (Federer et al,.1963). Senath (1977 used the OVL coefficients as a measure of disjunction of OVL measure on income differentials (see Mulekar and Mishra, 1994), Fukaswa, 2010 andInman andBradley, 1989).…”

On Inference of Overlapping Coefficients in Two Inverse Lomax Populations

“…Mishra et al [7] gave small and large sample properties of the sampling distribution for a function of Δ under the assumption of homogeneity of variances. Recently, several authors including Al-Saidy et al [8], Clemons [9], Dhaker et al [10], Inman and Bradley [11], Jose et al [12], Mulekar and Mishra [13] and Reiser and Faraggi [14] considered this measure.…”