Recurrence Relations for Moment Generating Functions of Generalized Order Statistics from Some Specific Continuous Distributions

Recurrence Relations for MGeneralized 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 some recurrence relations satisfied by the moment generating functions of generalized order statistics from pth order exponential distribution, left truncated logistic distribution and extreme value distribution. In all the above distributions, the corresponding recurrence relations for single and product moments of generalized order statistics have also been deduced.