New Lifetime Alpha Power Exponential Weibull Distribution: Structure and Properties - Hiba Mahdi Saleh; Ali Talib Mohammed; Umar Yusuf Madaki (Ibn Al-Haitham Journal for Pure and Applied Sciences)
In statistics theory, adding a new parameter is considered one of the important things that help in producing statistical distributions more flexible and appropriate in data analysis. Alpha-power transformations are considered a modern technique that involves adding a shape parameter to generate new statistical distributions. In this paper, a new life continuous distribution of three parameters is presented by fitting the alpha power transformations family distribution with two parameters lifetime exponential Weibull distribution. The new model named alpha-power exponential Weibull distribution (APEWD) with three parameters , where  and  are classified as scale parameters and  parameter is classified as a shape parameter. The cumulative, probability density, survival, hazard functions, and statistical properties of the proposed new model distribution were discussed and studied such as quantile function, moment about origin, moment generating function, Skewness, Kurtosis, factorial moments generating function, and characteristic function. To expand the probability density function for the new distribution, we took advantage of expanding the exponential function for ease of dealing with finding statistical properties