A New Three-Parameter Flexible Unit Distribution and Its Quantile Regression Model

Abstract

This paper introduces a novel Poisson-unit-Weibull (PUW) distribution, which is defined on a unit domain and characterized by three parameters. The PUW distribution is capable of accommodating diverse non-monotone failure rates. The paper explores several significant statistical properties of the model, including the explicit closed-form expressions for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r^{th}$ </tex-math></inline-formula> moments, quantile function, and Shannon entropy. The parameters of the PUW distribution are estimated using maximum likelihood estimation (MLE) and Bayes estimation with a square error loss function. The performance of these estimation methods is evaluated through Monte Carlo simulation studies. Furthermore, the paper discusses the practical aspects of the PUW-quantile regression model and its MLE, employing residual analysis in simulation studies. The flexibility of the PUW and PUW-quantile regression model is demonstrated through six real-life applications, showcasing their superior performance when compared to other popularly used models.