A new Beta distribution with interdisciplinary data analysis

Abstract

Several families of Beta distributions, such as Beta of the first kind, Beta of the second kind, and Beta of the third kind, have been proposed in the literature for modeling random phenomena. This study introduced a new member of the Beta family called the New Beta (NE-Beta) distribution using a logarithmic transformation approach. This new model is highly flexible and capable of analyzing both positive and negative data, making it suitable for a wide range of interdisciplinary applications. The NE-Beta distribution exhibits nearly symmetric, right-skewed, or left-skewed density functions and featured an increasing or decreasing hazard functions, which are crucial for accurately modeling practical scenarios across various fields. Some properties of the new distribution were derived, and the parameter estimation was obtained by utilizing various approaches. To demonstrate the efficacy of the NE-Beta distribution, it was applied to multiple datasets, including exchange rate returns (finance), biomedical data, engineering reliability data, and hydrological data. The results indicate that the proposed NE-Beta model outperforms its competitors across these diverse domains.