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On the Distribution of the Product and the Sum of Generalized Shifted Gamma Random Variables

Pushpa N. Rathie, Arjun K. Rathie and Luan C. de S. M. Ozelim

In general, while obtaining the probability density fun tion of sums and produ ts of shifted random variables, ordinary analyti al methods su h as Fourier and Mellin transforms tend to provide integrals whi h annot be expressed in terms of ordinary Meijer G and H fun tions. This way, the need of dening new fun tions whi h easily enable one to write su h integrals in a losed-form is inherent to the development of this area of statisti al s ien es. By generalizing the Mellin transform whi h denes the H fun tion, a new fun tion is established. A dire t appli ation of the so- alled Ib is dis ussed while developing the probability density fun tion of the sum and the produ t of shifted generalized gamma random variables. Important spe ial ases of the Ib and their appli ations in s ien e are also dis ussed in order to show the appli ability of the fun tion hereby dened.