On Explicit Expressions for Single and Product Moments of Generalized Order Statistics from a New Class of Exponential Distributions and a Characterization

Generalized order statistics

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 paper, we establish exact expressions for single and product moments of generalized order statistics from a new family of exponential distributions. We also give a characterization result for this class of distributions.