Generating families of distributions using Yun and sigmoidal transformations with an application to exponential...

Modeling complex data in modern applications demands highly flexible probability distributions capable of capturing diverse patterns in behavior. This study presents a novel framework for generating flexible families of distributions by incorporating useful mathematical functions. The proposed method, termed the QT-transformation, is built by combining a quantile function $Q(\cdot )$ with a continuous function $T(\cdot )$ . Using this approach, we construct two distinct families of distributions based on the Yun and sigmoidal transformations and analyze two sub-models derived from the exponential distribution as the baseline. Structural properties such as skewness, kurtosis, reliability characteristics, and tail behavior are thoroughly examined. The proposed models are shown to belong to several important classes of distributions. Parameter estimation is carried out using both the maximum likelihood estimation (MLE) and maximum product spacing (MPS) methods, and asymptotic confidence intervals are also constructed. The performance of the estimators is evaluated through extensive Monte Carlo simulations based on absolute bias, mean squared error, and confidence interval length. Finally, the practical utility of the proposed models is demonstrated through applications to two real-world datasets. Thus, the study introduces a unified and versatile distribution-generating mechanism that enhances lifetime analysis capabilities and offers broad applicability across statistical disciplines.