Abstract
This article review some known bivariate and bilateral (difference) gamma distributions. Some properties, advantages and limitations are pointed out. Two new bivariate gamma distributions using self-decomposability property are introduced. The corresponding bilateral gamma distributions are derived.
Highlights
In many real-life applications, more than one variable are collected on each individual
This distribution is known as double gamma distribution DBΓ(α1, α2, 1,1)
Let Y~Γ(α, 1) it is well known from the self-decomposability of gamma distribution that for every 0 < ρ < 1 there exists two independent random variables X~Γ(α, 1) and Xρ such that Y = ρX + Xρ where Xρ~CENB(α, ρ)
Summary
In many real-life applications, more than one variable are collected on each individual. Holm and Alouini (2004) have introduced the difference of two independent gamma random variables for the case of equal shape parameters They proved that it followed the second of MckKay’s (1932) distribution and computed the moments and the cumulative distribution functions. Küchler and Tappe (2008a) considered the distribution of the difference between two independent gamma random variables with different shapes and scales parameters and refered to it as bilateral gamma distribution. They studied some of its properties such as moments, self-decomposability, and closeness under convolution. We denote this compound exponential negative binomial distribution by CENB(α, ρ)
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