Simulation results.

In practical scenarios, data measurements like ratios and proportions often fall within the 0 to 1 range, posing unique modeling challenges. While beta and Kumaraswamy distributions are widely used, alternative models often yield better performance, though no clear consensus exists. This paper introduces a new bounded probability distribution based on a transformation of the Weibull distribution, with properties such as moments, entropies, and a quantile function. Additionally, we have developed the sequential probability ratio test (SPRT) for the proposed model. The maximum likelihood estimation method was employed to estimate the model parameters. A Monte Carlo simulation was conducted to evaluate the performance of parameter estimation for the model. Finally, we formulated a quantile regression model and applied it to data sets related to risk assessment and educational attainment, demonstrating its superior performance over alternative regression models. These results highlight the importance of our contributions to enhancing the statistical toolkit for analyzing bounded variables across different scientific fields.