The Bivariate Transmuted Family of Distributions: Theory and Applications

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way to model models. The bivariate families of distributions are not much widely explored and in this article a new family of bivariate distributions is proposed. The new family will extend the univariate transmuted family of distributions and will be helpful in modeling complex joint phenomenon. Statistical properties of the new family of distributions are explored which include marginal and conditional distributions, conditional moments, product and ratio moments, bivariate reliability and bivariate hazard rate functions. The maximum likelihood estimation (MLE) for parameters of the family is also carried out. The proposed bivariate family of distributions is studied for the Weibull baseline distributions giving rise to bivariate transmuted Weibull (BTW) distribution. The new bivariate transmuted Weibull distribution is explored in detail. Statistical properties of the new BTW distribution are studied which include the marginal and conditional distributions, product, ratio and conditional momenst. The hazard rate function of the BTW distribution is obtained. Parameter estimation of the BTW distribution is also done. Finally, real data application of the BTW distribution is given. It is observed that the proposed BTW distribution is a suitable fit for the data used.