Geodesic
The $I$-function distribution and its extensions
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 2, pp. 284-305 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, likelihood ratio statistics.
Mots-clés : Laplace transform 
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P. Vellaisamy; K. K. Kataria. The $I$-function distribution and its extensions. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 2, pp. 284-305. http://geodesic.mathdoc.fr/item/TVP_2018_63_2_a3/

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