Bivariate Nadarajah-Haghighi distribution derived from copula functions: Bayesian estimation and applications

Abstract

The Nadarajah-Haghighi distribution is an important lifetime distribution in survival analysis that serves as an alternative to the Weibull, gamma and exponentiated exponential distributions. In this paper, a new bivariate distribution is introduced using the Nadarajah-Haghighi distribution. The joint probability density function was obtained using two copula functions: Gumbel-Barnett and Clayton copula functions. The model was implemented under a Bayesian method of estimation, where Markov Chain Monte Carlo (MCMC) simulations technique was employed to estimate the parameters of the model. Applications to real data sets to show the utility of the model was provided using kidney data and diabetic retinopathy data sets. The results of the applications suggest that the new bivariate distribution fit the real data and perform much better than its competitors.