Characterizations of continuous probability distributions occurring in physics and allied sciences by truncated moment

Abstract

A probability distribution can be characterized through various methods. Before a particular probability distribution model is applied to fit the real-world data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterization. In this paper, characterizations of some continuous probability distributions occurring in physics and allied sciences have been established. We have considered the normal, Laplace, Lorentz, logistic, Boltzmann, Rayleigh, log-normal, Maxwell, Fermi-Dirac, and Bose-Einstein distributions, and characterized them by applying a truncated moment method; that is, by taking a product of reverse hazard rate and another function of the truncated point. It is hoped that the proposed characterizations will be useful for researchers in various fields of physics and allied sciences.