The I-Function Distribution and its Extensions

TL;DR

This paper introduces the I-function distribution, a new flexible distribution on (0,1) that generalizes many known distributions, and explores its properties, including products, quotients, powers, and an inverse Gaussian extension.

Contribution

It presents the I-function distribution and its extensions, providing new tools for modeling positive data with flexible distributional properties.

Findings

The I-function distribution generalizes several known distributions.

Products, quotients, and powers of I-function variates are also I-function variates.

Introduction and analysis of the I-function inverse Gaussian distribution.

Abstract

In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that the distribution of products, quotients and powers of independent I-function variates are I-function variates. Another distribution called the I-function inverse Gaussian distribution is also introduced and studied.