Bivariate Weibull Distribution: Properties and Different Methods of Estimation

Abstract

The bivariate Weibull distribution is an important lifetime distribution in survival analysis. In this paper, Farlie–Gumbel–Morgenstern (FGM) copula and Weibull marginal distribution are used for creating bivariate distribution which is called FGM bivariate Weibull (FGMBW) distribution. FGMBW distribution is used for describing bivariate data that have weak correlation between variables in lifetime data. It is a good alternative to bivariate several lifetime distributions for modeling real-valued data in application. Some properties of the FGMBW distribution are obtained such as product moment, skewness, kurtosis, moment generation function, reliability function and hazard function. Three different estimation methods for parameters estimation are discussed for FGMBW distribution namely; maximum likelihood estimation, inference function for margins method and semi-parametric method. To evaluate the performance of the estimators, a Monte Carlo simulations study is conducted to compare the preferences between estimation methods. Also, a real data set is introduced, analyzed to investigate the model and useful results are obtained for illustrative purposes.