New bounded probability model: Properties, estimation, and applications

The article introduces a new unit distribution, an extension of Tiessier distribution, characterized by a versatile hazard function capable of adopting diverse shapes such as bathtub or N-shaped curves. An exploration of the fundamental properties of this distribution is undertaken, accompanied by the implementation of the maximum likelihood estimation technique and eleven alternative methods to approximate its parameters effectively. Through a simulation study, the article effectively demonstrates the precision of these parameter estimation methods, even when dealing with small sample sizes. Two datasets are employed to apply the novel distribution, subjecting it to a comprehensive evaluation against established models utilizing a range of model selection criteria and goodness of fit tests. Notably, the article illustrates that the performance of the new distribution surpasses that of existing models in effectively capturing data patterns. Beyond its empirical contributions, the article highlights the potential cross-disciplinary applications of the new distribution in many fields while concurrently advancing the realms of probability theory and statistical inferences.