Several statistical distributions have been used profoundly for modeling real-life phenomena and have acquired significant attention in the recent literature. The potential of statistical distribution for modeling environmental sciences data is evident from the novel studies. The alpha power transformation (APT) method is considered a flexible and versatile approach and has been used quite effectively for the purpose of data analysis in recent years. In this paper, a new version of APT method has been proposed by extending the power “ \(\alpha\) ” by introducing the weight function. We call this new method as weighted alpha power transformation (WAPT) method. For illustrative purpose of the new WAPT method, a three-parameter special model of this class, namely, alpha power modified Weibull (APMW) distribution has been considered in detail. The proposed distribution offers greater distributional flexibility and is capable of modeling data with monotonic and non-monotonic failure rates. Various statistical properties of the proposed distribution have been studied. The value of the model parameters is estimated by using the method of maximum likelihood estimation. A simulation study based on complete sample of the proposed distribution is also carried out. Finally, four real life dataset from different fields of applied sciences like reliability, medical and environmental have been evaluated to show the applicability of the proposed model in practice.
