Bivariate exponentiated half logistic distribution: Properties and application

The exponentiated half logistic (EHL) distribution can be mostly and effectively used in modeling lifetime data. It is very similar to the gamma and exponentiated exponential distributions with two parameters. The major advantage of EHL distribution over the gamma distribution is that its cumulative distribution has a closed form. In this research, we develop a new bivariate exponentiated half logistic (BEHL) distribution with univariate EHL distribution as the marginals. The joint probability density function and the joint cumulative distribution function were expressed in explicit forms. This article also presents the various properties of the proposed distribution such as marginal, conditional distributions and product moments. The maximum likelihood estimates for the unknown parameters of BEHL distribution and their approximate variance- covariance matrix have been obtained. Monte Carlo simulations have been conducted to check the performances of the maximum likelihood estimators with applications to a real data set. Analysis showed that the BEHL distribution gives a better fit than other rival bivariate probability models.