A bivariate distribution with generalized exponential conditionals

In this work, we construct a new bivariate statistical distribution by the conditionally specified model approach. The conditional distributions follow the well-known generalized exponential distribution which includes the ordinary exponential distribution and is more flexible than gamma and Weibull in some ways. The newly defined distribution has four parameters that increase the flexibility of the model in data fitting. By equating the dependence parameter to zero, the marginal distributions become independent generalized exponential distributions. The new bivariate distribution depends on the classical exponential integral function which is not difficult to evaluate numerically. The basic properties of the distribution such as distribution functions, moments and stress-strength reliability are derived. The parameters are estimated by the method of maximum likelihood. Two real data fitting applications prove its usefulness in case of negatively correlated bivariate data modelling.