Abstract
A new family of continuous probability distributions is proposed by using Kumaraswamy-G distribution as the base line distribution in the Marshall-Olkin construction. A number of known distributions are derived as particular cases. Various properties of the proposed family like formulation of the pdf as different mixture of exponentiated baseline distributions, order statistics, moments, moment generating function, Rényi entropy, quantile function and random sample generation have been investigated. Asymptotes, shapes and stochastic ordering are also investigated. Characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function are also presented. The parameter estimation by method of maximum likelihood, their large sample standard errors and confidence intervals and method of moment are also discussed. Two members of the proposed family are compared with different sub models and also with the corresponding members of Kumaraswamy-Marshall-Olkin-G family by fitting of two real life data sets.
Highlights
One of the preferred area of research in the filed of the probability distribution is that of generating new distributions starting with a base line distribution by adding one or more additional parameters
We propose a new extension of the MO family by considering the cdf and pdf of Kw-G distribution in (4) and (5) as the f (t) and F (t) respectively in the MO formulation in (3) and call it Marshall-Olkin Kumaraswamy-G (MOKw-G) distribution with pdf given by f MOKwG (t) = a a b g(t)G(t) a−1[1 − G(t) a ] b−1 [1 − a [1 − G(t) a ] b ] 2, − ∞ < t < ∞, a > 0, a > 0, b > 0 . (6)
Equations (11)-(16) reveal that the density functions of the MOKw-G distribution and that of its order statistics can be expressed as a product of the baseline density f (t) with an infinite power series of G (.) and as a mixture of exponentiated-G distributions under Lehman alternatives
Summary
One of the preferred area of research in the filed of the probability distribution is that of generating new distributions starting with a base line distribution by adding one or more additional parameters. It is obvious that many new families can be derived from Marshall-Olkin set up by considering different base line distribution F in the equation (1). The main motivation behind the present article is to propose a new family of continuous probability distributions that generalizes the Kw-G family as well as the Marshall-Olkin extended family by integrating the former as the base line distribution in the latter. We call this new family the Marshall-Olkin Kumaraswamy-G (MOKw-G) family of distributions which encompasses many known families of distributions and study some of its general properties, characterizations and parameter estimation. The paper ends with concluding remarks in the final section
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