Bivariate Chen Distribution Based on Copula Function: Properties and Application of Diabetic Nephropathy

The purpose of this paper is to create a new bivariate model with more efficiency than the traditional models which discuss the effect of serum creatinine given the duration of diabetes. Based on FGM copula function and Chen distribution, we will introduce the bivariate FGM Chen distribution. Marginal distributions, product moments, and moment generating functions are studied as some of their statistical properties. Some dependency tests, such as Kendall's tau, Pearson's correlation, and regression model, are discussed. To estimate the model parameters, maximum likelihood and Bayesian estimation are used. In addition, for the parameter model, asymptotic confidence intervals and credible intervals of the highest posterior density for the Bayesian are calculated. A Monte Carlo simulation analysis is carried out of the maximum likelihood and Bayesian estimators.