A REVIEW OF CONTINUOUS UNIVARIATE PROBABILITY DISTRIBUTIONS FROM PEARSON'S FAMILY OF DISTRIBUTIONS TO THE COMPOSITE FAMILY OF DISTRIBUTIONS

Abstract

Seeking the flexibility of probability distributions in modeling real life phenomena could be adjudged as the driving force behind the development of new probability distributions. Methods for generating families of continuous univariate probability distributions have received widespread attention in recent decades. It is well established that much of practical statistical studies and developments in probability theory have been dominated by the normal distribution for several decades. However, in the late 19th century, the increasing collection, tabulation, and publication of data by government, private institutions and agencies in demography, social sciences, biology and insurance revealed that the normal distribution was not sufficient for describing phenomena (homogenous with respect to all but random factors) in the real world situations. This reality spearheaded the need to develop other families of distributions that can be well adapted to real-life problems. In this paper, a review of families of continuous univariate probability distributions from the Pearson's family down to the composite family of distributions.