A Generalization of Additive Weibull Distribution And Its Properties

Additive Weibull 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.

We introduce a new family of distributions by using truncated discrete
Mittag-Leffler distribution. Some properties of this family of distributions are studied. As a particular case, we study discrete Mittag-Leffler additive Weibull distribution. This distribution contains several well-known distributions such as Marshall-Olkin additive Weibull distribution, Marshall-Olkin Weibull distribution, Marshall-Olkin Rayleigh distribution, Marshall-Olkin generalized exponential distribution, exponentiated Weibull distribution, Marshall-Olkin exponential distribution, generalized exponential distribution, Weibull distribution, exponential distribution etc. The shape properties, moments, distributions of the order statistics, entropies are derived and estimation of the unknown parameters are considered. An application to a real data is also presented.