Mixture Model on Development of Bivariate Product Distribution and its Properties

In the study, some bivariate distributions were developed from mixture model offspring, using the Independent (Product) distribution approach. These developments are categorized under the IID and IInD: where the Bivariate Exponential distribution, Bivariate Lindley distribution and Bivariate Juchez distribution are constructed as IIDs; and Bivariate Exponential-Lindley distribution, Bivariate Exponential-Juchez distribution and Bivariate Lindley-Juchez distribution as (IInDs). The properties of these distributions which involve: the shape of the bivariate PDFs, moments, moment generating function, mean, covariance and coefficient of correlation, maximum likelihood estimator, reliability analysis, renewal property and probability patterns; are studied across the distributions. Finally, under renewal properties, functions are derived which can model two-dimensional queuing and renewal processes, for events where the arrival and service times are dependent.