This article is cited in 12 papers

The $I$-function distribution and its extensions

P. Vellaisamy, K. K. Kataria

Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, India

Abstract: In this paper we introduce a new probability distribution on $(0,\infty)$ associated with the $I$-function, and hence called the $I$-function distribution. This distribution generalizes several known distributions with positive support (see the table at the end of the paper). It is also shown that the product, quotient, and rational power of independent random variates with $I$-distribution are random variates with $I$-distribution. Another new distribution—the $I$-function Gaussian distribution ($IFIG$ distribution)—is introduced and defined in terms of the $I$-function. For this distribution, the representations of its Mellin and Laplace transforms are obtained. The utilities of the $I$-function distribution are discussed with an application to the likelihood ratio statistic.

Keywords: $I$-function, $H$-function, Mellin transform, Laplace transform, likelihood ratio statistics.

Received: 18.11.2015
Revised: 31.01.2018

Language: English

DOI: 10.4213/tvp5184

 English version: Theory of Probability and its Applications, 2018, 63:2, 227–245

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