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Daya K. Nagar, Edwin Zarrazola, Johanna Marcela Orozco-Castaneda,

Product and quotient of independent Topp-Leone variables.

Int. J. Math. Comput. Sci., 20, no. 2, (2025), 641-649

DOI:

https://doi.org/10.69793/ijmcs/02.2025/EdwinZarrazola

Keywords and phrases:

Appell's first hypergeometric function, Beta distribution, gamma distribution, Gauss hypergeometric function, Humbert hypergeometric function, Lauricella hypergeometric function, product, quotient, Topp-Leone distribution, transformation.

Abstract:

The univariate family of Topp-Leone distributions has been studied recently by a number of researchers. This distribution has finite support and possesses many interesting properties. In this article, we derive the exact distributions of X_1X_2, X_1/X_2 and X_1/(X_1+X_2) when X_1 and X_2 are independent Topp-Leone/beta variables. The resulting distributions are expressed in terms of special functions.