Modal truncated Weibull regression model for modeling differences in rates or proportions

In this paper, we introduce a transformation of the truncated Weibull distribution, originally defined in the interval $(0,2)$ , to facilitate the analysis of differences between rates or proportions. The transformed distribution is defined on the interval $(-1,1)$ and parameterized in terms of its mode and shape parameters. We refer to this new distribution as the modal truncated Weibull (MTW) distribution. Building on the MTW distribution, we propose a novel modal regression model in which the parameters are estimated using the maximum likelihood method. To assess the performance of the maximum likelihood estimators, we conducted a Monte Carlo simulation study under various scenarios and regression structures. Additionally, we derive analytical expressions for the score vector and the Fisher information matrix, providing a foundation for parameter estimation and inference. We also briefly discuss diagnostic tools for evaluating the fit and performance of the model. Finally, we present and analyze an empirical application to demonstrate the practical utility and relevance of the proposed MTW regression model.