On Xbeta distribution: properties, estimation and application

Resumen

BackgroundUseful instruments for evaluating the randomness of events in life are probability models. Although the literature contains many statistical distributions, it is always possible to obtain more powerful, more adaptable distributions with more general applications. For estimation and prediction, these probability models are priceless. Current probability models do not always offer the best match since a great deal of new data is available. By generalizing or presenting novel probability models that can be simply matched to these latest data sets, researchers have substantially added to the body of knowledge. The objective of this research is introducing new probability distributions; this is done by several methods and usually by adding new parameters to an existing distribution. MethodsA flexible distribution called the Xbeta distribution is proposed for analyzing bounded data. Key characteristics, including the shape of the model, survival and hazard functions, and analytical expressions of mode, quantile function, ordinary moments, and stress-strength reliability, are comprehensively analyzed. Additionally, several famous entropy measures are derived.
ResultsThe Xbeta model parameters have been estimated using four distinct methods: maximum likelihood estimation, Anderson-Darling, Cramer-von Mises, and ordinary least squares. A detailed simulation study is used to evaluate the behavior of all derived estimators. Finally, a dataset is used to demonstrate the utility of the proposed distribution. ConclusionThe value of the new distribution is demonstrated using a dataset linked to flood level and polyester fiber tensile strength measurements. Goodness-of-fit tests led to the conclusion that the Xbeta distribution effectively analyzed these data sets relatively to competing distributions.