Weibull Sine Generalized Distribution Family: Fundamental Properties, Sub-model, Simulations, with Biomedical Applications

Abstract

This study explores the integration of trigonometric functions into traditional statistical models, focusing on the development of the Weibull Sine Generalized (WSG-G) family of distributions. A special case was formulated name Weibull Sine generalized exponential (WSG-E) distribution. This new distribution extends the baseline exponential distribution, accommodating heavier tails and outliers, thereby effectively modeling positively skewed data. Key statistics such as mean, variance, skewness, and kurtosis indicate the distribution's capacity to handle clustered data. A simulation study demonstrates the performance of Maximum Likelihood Estimation (MLE), revealing convergence in the mean squared error and root mean squared error for the parameter \( \alpha \) with increasing sample sizes, although convergence is less evident for other parameters. The WSG-E distribution's applicability is further illustrated through its fitting of medical datasets on bladder cancer remission times and growth hormone deficiency in children, both characterized by extreme values. Overall, the WSG-E distribution proves to be a robust model for skewed data, and future research could extend this framework to additional continuous distributions.