A Generalized Form of Power Transformation on Exponential Family of Distribution with Properties and Application

In this paper, we proposed a new generalized family of distribution namely alpha power Exponential (NAPE) based on the transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties are obtained including moment, incomplete conditional probability weighted moments (PWMs), quantile function, residual and reversed lifetime stress-strength parameter, entropy order statistics. The percentage point NAPE for some specific values parameters is also obtained. maximum likelihood estimation (MLE) has been used estimating distribution. A simulation study performed to evaluate execute behavior estimated mean square errors (MSEs) bias. Finally, efficiency flexibility model illustrated analyzing three real-life data sets.