A New Bivariate Distribution with Modified Weibull Distribution as Marginals

A new bivariate distribution with modified Weibull distribution as marginals is introduced. The joint survival function, joint probability density function, marginal and conditional probability density functions, moments and moment generating function are derived. The bivariate reliability function, joint hazard rate function, mean waiting time and the reverse hazard rate function of the new bivariate distribution are obtained. The maximum likelihood estimators of the unknown parameters are obtained. A simulation study is conducted to show the performance of the maximum likelihood estimates of the parameters. An application of this distribution to a real data set is illustrated. Bivariate copula function for the new distribution is proposed. © 2018, The Indian Society for Probability and Statistics (ISPS).