A New Generalization of Inverse Marshall-Olkin Family and Related Inverse Exponential Model

A new generalization of inverse Marshall-Olkin family

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 continuous distributions called inverse truncated discrete Mittag-Leffler family of distributions. In particular, we study inverse truncated discrete Mittag-Leffler exponential (GIE) distribution. The GIE distribution contains inverse Marshall-Olkin exponential distribution, inverse generalized exponential distribution and inverse exponential distribution as special case. The density function of GIE distribution is right skewed and has reverse bathtub hazard rate. We derive expression for the moments, generating function, quantiles and R´enyi entropy. Also the stochastic ordering properties are investigated along with the distributions of order statistics. The method of maximum likelihood is used to estimate the model parameters. The existence and uniqueness of maximum likelihood estimates are proved. Simulation studies are also performed. An application to a real data set is presented to illustrate the potentiality of our proposed model.