On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates
Keywords:Exponential Distribution, Nadarajah-Haghighi Distribution, Bivariate Models and Copula Function.
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 distribution
is an extension of the well known exponential distribution. In this paper, a copula
function 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 given
in closed form. Bayesian method of estimation was used to estimate the model
parameters considering the presence of right censoring and covariates. Posterior
summaries 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 was
observed that, the bivariate Nadarajah-Haghighi distribution provides a better flt
than bivariate exponential, bivariate Weibull, bivariate generalized exponential
and bivariate modified Weibull distributions.
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