On A Generalized Class Of Weibull Distribution And Its Applications

On a generalized class of 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 paper, we propose a family of continuous distributions called odds X Weibull(OXW) distributions using the T-X family concept introduced in Alzaatreh et al. (2013). Some of the special models of this family are introduced and one among them, odds exponential-Weibull(OEW) distribution is studied in detail. This distribution is found to be a competitor for the well known lifetime models such as exponential, Weibull, exponentiated exponential, exponentiated Weibull, etc. The method of maximum likelihood is used for estimating the model parameters and a simulation study is carried out to check the performance of the method. Time series models with OEW distribution as marginals are developed. Two real data sets are used to illustrate the applications and flexibility of the OEW distribution.