COMPLEMENTARY GENERALIZED TRANSMUTED POISSON LOMAX DISTRIBUTION WITH ITS DERIVED PROPERTIES AND APPLICATION

Abstract

There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. In this research, a new four parameter lifetime distribution which extends the Lomax distribution is introduced by compounding the Lomax distribution with the complementary generalized transmuted Poisson family of distributions. The probability density function and cumulative distribution function as well as some basic statistical properties of the new distribution, such as moments, reliability function, hazard function, quantile function, residual life function, entropy and the order statistics were derived. Some plots of the distribution shows that it is a positively skewed distribution. The maximum likelihood estimation method is used to estimate the parameters of the new distribution. A simulation study to assess the performance of the parameters of the newly developed distribution was provided with an application to real life data to assess its potentiality. The result shows that the proposed distribution provides better fit than some generalizations of the Lomax .

Keywords: Lifetime distribution, maximum likelihood estimation, Lomax distribution, hazard    function, order statistics.