On the Bivariate Generalized Gamma-Lindley Distribution

Abstract

ABSTRACT In this research paper, we propose a new class of bivariate distributions called Bivariate Generalized Gamma-Lindley (BGGL) distribution with four parameters. This model is a mixture of independent Gamma random variables and bivariate generalized Lindley distribution. We investigate various properties of the new bivariate distribution such as graphical representation, joint moments and correlation. Furthermore, we derive a measure of entropy of this bivariate distribution. We also derive the distributions of the random variables X 1 + X 2, X 1/(X 1 + X 2), X 1/X 2 and X 1 X 2 as well as the corresponding moment properties when X 1 and X 2 follow the BGGL distribution. Additionally, we address two approximations of the product of the proposed model and assess their goodness of fit. Next, we elaborate the expectation maximization (E.M) algorithm in order to estimate the BGGL model parameters. Finally, we provide two concrete examples to demonstrate the applicability of the results.