A New Bivariate Distribution with Extreme Value Type I and Burr Type XII Distributions as Marginals

Extreme-Burr Impounded Bivariate Distribution

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

In this work, we develop a new bivariate distribution by assuming a specified distribution to one marginal random variable and a specified distribution to the concomitant of the largest order statistic on the other random variable. We also discuss about the role of concomitants of lower record values in the construction of the above bivariate distribution. We assume the form of distribution of one marginal random variable and the distribution of the concomitant of the largest order statistic in such a way that the resulting bivariate distribution is one with extreme value type I and Burr-Type XII distributions as its marginals. Some general characteristics of this newly generated distribution are studied. The method of maximum likelihood is applied for the estimation of the parameters of the generated distribution. We have identified the generated model as a suitable model for two real life bivariate data sets reported in the literature.