Point Estimation of Pianka and Kullback-Leibler Overlapping Coefficients: Two Normal Distributions
Department of Statistics, Yarmouk University, Irbid 21163, Jordan
| Abstract: | The well-known two overlapping coefficients; Pianka and Kullback-Leibler are considered to be important measures that focus on measuring the closeness or similarity between two continuous or discrete probability distributions. A general expression for each of them has been developed for some statistical distributions, such as exponential distribution and Weibull distribution. In this research, we focused on the most famous statistical distribution, which is the normal probability distribution.Our main contribution in this paper is to derivation and estimation the two overlapping coefficients Pianka (PI) and Kullback-Leibler (KL) under the assumption of existing a pair of normal distributions. The mathematical formulas (parameters) for each of the PI and KL coefficients were obtained without imposing any restrictions on the parameters of the pair normal distributions. To complete the estimation process of each resulting parameter, an estimator was proposed for each of them by deriving the maximum likelihood estimator based on the assumption of existing two independent random samples, each following the statistical normal distribution. |
| Keywords: | Overlapping Coefficient; Pianka Coefficient; Kullback-Leibler Coefficient; Maximum Likelihood Estimation Method; Normal Distribution |
| DOI: | 10.57237/j.wjms.2025.01.001 |
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Received: 5 October 2024
Accepted: 19 November 2024
Published Online: 2 January 2025
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