The SAS-Transformation for Generating Distributions: Properties and Application to the Power Function Model

This study introduces a novel transformation based on the cumulative distribution function, termed the Shantanu, Arun, Shubham (SAS)-transformation, for generating a flexible class of probability distributions. The primary objective is to develop a general framework that enhances modeling capability for bounded data. As a special case, the transformation is applied to the power function distribution to construct a new SAS-power function model. The statistical properties of the proposed model are derived, including the survival and hazard rate function, moments, conditional moments, quantile function, mean deviation, order statistics, entropy, and stochastic ordering. A comprehensive simulation study is conducted to assess the performance of classical estimation methods, demonstrating that the estimators perform efficiently in terms of Bias and mean squared error under various parameter settings. The practical usefulness of the proposed model is illustrated through real data applications, where it provides improved goodness-of-fit compared to existing models, as evidenced by criteria such as Akaike Information Criterion, Corrected Akaike Information Criterion, Bayesian Information Criterion, log-likelihood, and Kolmogorov–Smirnov test. These findings highlight the flexibility and applicability of the SAS-transformation in statistical modeling, particularly for lifetime and reliability analysis.