On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates

Abstract

An important alternative distribution to the Weibull, generalized exponen-tial and gamma distributions that is used in survival analysis is the Nadarajah-Haghighi exponential distribution. Similar to the Weibull, generalized exponen-tial and gamma distributions, the Nadarajah-Haghighi exponential distributionis an extension of the well known exponential distribution. In this paper, a copulafunction commonly used to model very weak linear dependence was used to intro-duced a bivariate Nadarajah-Haghighi distribution. The joint survival function,joint probability density function and joint cumulative distribution were givenin closed form. Bayesian method of estimation was used to estimate the modelparameters considering the presence of right censoring and covariates. Posteriorsummaries of interest were obtained via standard Markov Monte Carlo (MCMC )technique. Two real data sets were used to illustrate the importance and flexi-bility of the bivariate model in comparison with some competing models. It wasobserved that, the bivariate Nadarajah-Haghighi distribution provides a better fltthan bivariate exponential, bivariate Weibull, bivariate generalized exponentialand bivariate modified Weibull distributions.