On a Generalization of Marshall-Olkin Weibull Distribution and its Applications

Generalization of Marshall-Olkin 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.

In this article, a new generalized four parameter distribution called Marshall- Olkin Weibull Truncated Negative Binomial (MOWTNB) distribution is introduced and studied. Various structural properties of the new distribution are obtained. The distribution of order statistics is also derived. The method of maximum likelihood for estimating the model parameters is discussed. Applications to two real data sets are provided to show the flexibility and potentiality of the new distribution. We have compared the performance of MOWTNB with ten other competitive models, for modelling the two data sets and showed that MOWTNB performs better compared to these existing models. An AR(1) minification model with this distribution as marginal is developed.