New Bivariate Exponentiated Modified Weibull Distribution

The new modified Weibull distribution named exponentiated modified Weibull distribution introduced by many authors. In this study, we define and study a bivariate modified Weibull distribution. Some joint probability functions and conditional probability density function are obtained. Also, joint survival function is expressed in compact form. Several statistical properties of this distribution are discussed. In the area of stress-strength models, we estimate the reliability follow a bivariate exponentiated modified Weibull distribution with dependence between stress and strength variables. Parameters estimators using the maximum likelihood method are obtained. Moreover, a numerical illustration is used to obtain Maximum Likelihood Estimators (MLEs).