A New Method for Generating Distributions with an Application to Exponential Distribution

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in details namely; one parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, order statistics and expression of the entropies are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Further we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes. Two data sets have been analyzed to show how the proposed models work in practice.