A Discrete Generalization of Marshall-Olkin Scheme and its Application to Geometric Distribution

Discrete generalization of Marshall-Olkin scheme

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 introduce a new family of discrete distributions and study
its properties. The new family is a generalization of discrete Marshall-Olkin
family of distributions. In particular, we study discrete generalized Marshall-
Olkin exponential (DGMOE) distribution in detail. Generalized geometric distribution and geometric distribution are sub-models of DGMOE distribution. We derive some basic distributional properties such as probability generating function, moments, hazard rate and quantiles of the DGMOE distribution. Estimation of the parameters are done using maximum likelihood method. A real data set is analyzed to illustrate the suitability of the proposed model.