The Power Exponential-G Family of Distributions: Properties and Applications

A new and flexible family of continuous probability distributions, Power Exponential-G family is presented in this paper.The proposed family exploits an additional shape parameter to improve the flexibility of modeling input data structures in practice and extends the basic distribution with a power exponential transform.This formulation offers a unified approach for developing new models that can accommodate a wide range of distributional forms, such as skewness, heavy tails and different hazard rate shapes.The general mathematical properties of the Power Exponential-G family are investigated in details, such as cumulative and probability density functions, moments, quantile function and reliability measures.To demonstrate the application of the developed framework a particular family member, namely, the Power Exponential Weibull distribution is derived and studied.Maximum-likelihood estimates of the parameters and statistical performance are assessed both theoretically and by means of Monte Carlo studies for a variety of parameter settings and sample sizes.To demonstrate practical applicability, the Power Exponential Weibull distribution is fitted to several real lifetime and reliability datasets and compared with well-known competing models.The comparative results, based on information criteria and goodness-of-fit statistics, reveal that the new model provides a more accurate and adaptable representation of empirical data.