Conditionally Specified Bivariate Kummer-Gamma Distribution

Abstract

The Kummer-gamma distribution is an extension of gamma distribution and for certain values of parameters slides to a bimodal distribution. In this article, we introduce a bivariate distribution with Kummer-gamma conditionals and call it the conditionally specified bivariate Kummer-gamma distribution/bivariate Kummer-gamma conditionals distribution. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities, and conditional moments. We also discuss several important properties including, entropies, distributions of sum, and quotient. Most of these representations involve special functions such as the Gauss and the confluent hypergeometric functions. The bivariate Kummer-gamma conditionals distribution studied in this article may serve as an alternative to many existing bivariate models with support on (0,∞)× (0,∞). Key-Words: Bivariate distribution; confluent hypergeometric function; gamma distribution; gamma function; Gauss hypergeometric function; Kummer-gamma distribution. Received: March 20, 2021. Revised: April 20, 2021. Accepted: April 22, 2021. Published: April 29, 2021.