On a New Class of Univariate Continuous Distributions that are Closed Under Inversion

Abstract

Inverted probability distributions find applications in various real – life situations including econometrics, survey sampling, biological sciences and life – testing. Closure under inversion implies that the reciprocal of a continuous random variable X has the same probability function as the original random variable, allowing for a possible change in parameter values. To date, only a very few probability distributions have been found to possess the closure property.

In this paper, an attempt has been made to generate a class of distributions that are closed under inversion, and to develop some statistical properties of this class of distributions.