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 Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 2, Pages 284–305 (Mi tvp5184)

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.

 Funding Agency Grant Number University Grants Commission F.2-2/98(SA-I) The research of the second author was supported by UGC fellowship F.2-2/98(SA-I), Government of India, and by the Industrial Research and Consultancy Centre (IRCC), IIT Bombay.

DOI: https://doi.org/10.4213/tvp5184

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

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Revised: 31.01.2018
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Citation: P. Vellaisamy, K. K. Kataria, “The $I$-function distribution and its extensions”, Teor. Veroyatnost. i Primenen., 63:2 (2018), 284–305; Theory Probab. Appl., 63:2 (2018), 227–245

Citation in format AMSBIB
\Bibitem{VelKat18} \by P.~Vellaisamy, K.~K.~Kataria \paper The $I$-function distribution and its extensions \jour Teor. Veroyatnost. i Primenen. \yr 2018 \vol 63 \issue 2 \pages 284--305 \mathnet{http://mi.mathnet.ru/tvp5184} \crossref{https://doi.org/10.4213/tvp5184} \elib{http://elibrary.ru/item.asp?id=32823082} \transl \jour Theory Probab. Appl. \yr 2018 \vol 63 \issue 2 \pages 227--245 \crossref{https://doi.org/10.1137/S0040585X97T989024} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000448195800004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056950093}