Bivariate exponentiated generalized inverted exponential distribution with applications on dependent competing risks data

This paper introduces a novel bivariate distribution derived from the univariate exponentiated generalized inverted exponential (EGIE) distribution, which we term the bivariate exponentiated generalized inverted exponential (BEGIE) distribution. The newly proposed distribution belongs to the Marshall-Olkin class. Several statistical attributes of the BEGIE distribution are explored. The utility of this distribution is examined through applications on both bivariate data and dependent competing risks data. Estimation processes for the model's parameters, using maximum likelihood and Bayesian methods, are outlined for scenarios involving both bivariate and dependent competing risks data. Due to the absence of closed-form solutions for these estimators, numerical optimization techniques are employed. Furthermore, the proposed distribution is illustrated and evaluated through the analysis of three real datasets: two involving bivariate data, and the other involving dependent competing risks data.