The Marshall-Olkin IKum Distribution

Finding alternative to most well known classical family of distributions has become a topic of high importance in academic research due to their striking properties. An increasing interest can be observed for the art of adding parameter to some existing distributions as one parameter family of distributions is not sufficient to handle various real contexts. There is a vast amount of literature on method of introducing new distributions. Several statistical experts have mentioned similar processes (exponentiated family of distributions (by Gupta et al. [1]), Kumaraswamy family of distributions (by Cordeiro and Castro [2]), Kummer beta generalized family of distributions (by Pescim et al. [3]), geometric exponential-Poisson family of distributions (by Nadarajah et al. [4]), exponentiated T-X family of distributions (by Alzaghal et al. [5]), Weibull generalized family of distributins (by Bourguignion et al. [6], modified beta generalized family of distributions (by Nadarajah et al. [7]) and exponentiated exponential-Poisson family of distributions (by Risti c′ and Nadarajah [8]).) with applications in various factual contexts as inclusion of new parameter to existing family of distributions increases flexibility of the distributions. Also data with a high degree of skewness and kurtosis can be modeled. Again it is helpful in improving the goodness of fit of proposed generalized family of distributions. We may use various methods to add new parameters for expanding family of distributions. Marshall and Olkin [9] introduced a general method, the resulting distribution is called Marshall-Olkin Extended (MOE) family of distributions, its cumulative density function (cdf) ( ) G x and probability density function (pdf) ( ) g x are given by the following formulae, ( ) ( , )= , , >0 (1 ) ( ) F x G x x R F x α α α α ∈ + − (1.1)