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Abstract In practical scenarios, data measurements like ratios and proportions often fall within the 0 to 1 range. Analyzing such bounded data introduces unique modeling challenges, prompting statisticians to explore new distributions that can effectively handle this context. Although beta and Kumaraswamy distributions, along with their related regression models, have gained popularity for examining the relationship between bounded response variables and covariates, several alternative models have shown superior performance compared to these two. However, there is still no agreement on the most effective alternative models. Consequently, this paper introduces a novel bounded probability distribution derived from transforming the Weibull distribution. Our investigation has revealed several interesting properties, including various moments and their generating function, entropies, quantile function, and a linear form of the proposed model. 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.
Sapkota et al. (Fri,) studied this question.