A Generalization of Additive Weibull Distribution And Its Properties
Additive Weibull distribution
Keywords:
Additive Weibull distribution, Discrete Mittag-Leffler distribution, Marshall-Olkin family of distributions, Truncated negative binomial distributionAbstract
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.
