Abstract

We propose a new method of adding two shape parameters to a family of distributions for more flexibility and wider scope of applications. The method involves the compounding of two family, namely the Poisson family and the Type-2 Topp Leone family resulting in a flexible family called the Type-2 Topp Leone Poisson-g distribution. A special case of the family has been considered called Type-2 Topp Leone Poisson Burr XII distribution. Several properties of the proposed distribution are investigated, including explicit expressions for the moments, quantiles, moment generating function, mean and median deviation, mean residual and mean mean activity time, order statistics and expression of the Renyi and Tsallis entropies are derived. The maximum likelihood estimator technique is used to obtain the values of the unknown parameters. Simulation study is also carried out to determine the effectiveness of the maximum likelihood estimation technique. Two data sets have been analyzed to demonstrate the applicability of the proposed models in practice.

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