A New Trigonometric-Inspired Probability Distribution: The Weighted Sine Generalized Kumaraswamy Model with Simulation and Applications in Epidemiology and Reliability Engineering

The importance of statistical distributions in representing real-world scenarios and aiding in decision-making is widely acknowledged. However, traditional models often face limitations in achieving optimal fits for certain datasets. Motivated by this challenge, this paper introduces a new probability distribution termed the weighted sine generalized Kumaraswamy (WSG-Kumaraswamy) distribution. This model is constructed by integrating the Kumaraswamy baseline distribution with the weighted sine-G family, which incorporates a trigonometric transformation to enhance flexibility without adding extra parameters. Various statistical properties of the WSG-Kumaraswamy distribution, including the quantile function, moments, moment-generating function, and probability-weighted moments, are derived. Maximum likelihood estimation is employed to obtain parameter estimates, and a comprehensive simulation study is performed to assess the finite-sample performance of the estimators, confirming their consistency and reliability. To illustrate the practical advantages of the proposed model, two real-world datasets from epidemiology and reliability engineering are analyzed. Comparative evaluations using goodness-of-fit criteria demonstrate that the WSG-Kumaraswamy distribution provides superior fits compared to established competitors. The results highlight the enhanced adaptability of the model for unit-interval data, positioning it as a valuable tool for statistical modeling in diverse applied fields.