Derivation of Incomplete gamma functions properties with applications


Abstract


We derive some useful identities for the incomplete gamma functions using probabilistic techniques. In particular, we use distributions of order statistics from the gamma distribution to derive some identities that involve integration of functions of the incomplete gamma function. We use these properties to construct bivariate Gamma distributions.

Keywords: Gamma distributions, order statistics, hypergeometric function, Whittaker function, bivariate distributions, bivariate Gamma distributions

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