Some Characterizations of Harris Distribution

Harris 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.

The fact that Harris distribution is a member of generalized power series distribution gives rise to the characterizations based on the sensitivity of the reliability function, mean and variance, infinite divisibility and series function. Some other distributions with gaps in this support are also characterized.