Asian Journal of Probability and Statistics

The continuous development of flexible probability distributions has become essential for accurately describing complex stochastic phenomena. In this study, a new theoretical based on the New Sine Type II Generalized Topp-Leone distribution is investigated. The model is constructed by integrating the sine trigonometric transformation with the Type II Topp-Leone generator applied to an arbitrary baseline distribution. This combination introduces additional shape parameters that enhance the adaptability of the resulting family of distributions. Several mathematical properties of the proposed model are derived. These include explicit expressions for the cumulative distribution function (cdf), probability density function (pdf), survival function, and hazard rate function. In addition, analytical forms of the quantile function, moments, moment generating function, and order statistics are established. The author’s adopted two estimation techniques in this work: the maximum likelihood estimation (MLE) and the maximum product of spacing (MPLS) estimation methods. The structural characteristics of the distribution reveal that it is capable of producing a wide range of density and hazard rate shapes depending on the selected baseline model and parameter values. The theoretical results presented in this work provide a general framework for constructing new members of the family and offer a foundation for further statistical developments involving estimation techniques and practical implementations. Plots of the pdf, cdf as well as the validity check on the pdf of the new model indicate that the model is adequate capable of handling all the intricate associated with real-life datasets.