A New Family of Distributions with Exponentiated Modified Term
This paper introduces family of distributions by adding a special term to distribution function. This term is equipped with an extra parameter which provides to be more flexible family of distribution. Two new families of distributions are proposed by adding modified exponentiated term to product of two distribution functions. A special case, where baseline distributions of family are exponentials, has been considered in details. Some properties of the proposed distribution, including explicit expressions for the raw moments, moment generating function, hazard rate function are derived. Shapes and limit behavior of the hazard function are discussed. The maximum likelihood estimators of parameters cannot be obtained in explicit forms, so likelihood equations have to be solved by numerical methods only. Furthermore, three real data sets have been analyzed to show how the considered model work in practice.
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