The Bivariate Generalized Rayleigh Distribution

Authors : Ammar SARHAN

Pages : 99-111

Doi:10.33187/jmsm.439873

View : 14 | Download : 7

Publication Date : 2019-08-30

Article Type : Research Paper

Abstract :This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distribution insert ignore into journalissuearticles values(BVGR);. The proposed distribution is of type of Marshall-Olkin insert ignore into journalissuearticles values(MO); distribution. The BVGR distribution has  generalized Rayleigh marginal distributions. The joint cumulative distribution function,  the joint survival function, the joint probability density function and the joint hazard rate function of the proposed distribution are obtained in closed forms. Statistical properties of the BVGR distribution are investigated. The maximum likelihood and Bayes methods are applied to estimate the unknown parameters. Both maximum likelihood and Bayes estimates are not obtained analytically. Therefore, numerical algorithms are required to report on the model parameters and its reliability characteristics. Markov Chain Monte Carlo insert ignore into journalissuearticles values(MCMC); algorithm is applied for the Bayesian method. A real data set is analyzed using the proposed distribution and compared it with existing distributions. It is observed that the BVGR model fits this dataset better than the MO and the bivariate generalized exponential insert ignore into journalissuearticles values(BVGE); distributions.
Keywords : Marshal Olkin, multivariate distribution, shock models