Generalized Beta Distribution: Theoretical Properties and Applications in Health Data Modeling

Vollständiger Abstract

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In this publication, a generalization of the classical Beta distribution by five parameters, called the Generalized Beta (GB) distribution, is introduced and well examined, particularly on the usage of the health data. The GB distribution provides the highest flexibility ever in the modeling of complex data patterns in med and public health analyses including the incidence of illnesses, response to treatments, and the values of biomarkers. Systematically basic statistical properties, including correct formulations of moments, moment-generating functions, characteristic functions, hazard functions, and entropy measures, are obtained in this paper. The article gives novel recurrence relations of moments and incomplete moments, which are computationally useful in their application. The paper delves deep into correlation with other important statistical distributions like Kumaraswamy, generalized Gamma, Power Function and Mc-Donalds generalized distributions, by in-exhaustive mathematical analysis. This paper constructs robust parameter estimations practices on both frequentist (maximum likelihood), and in the Bayesian paradigm which have been examined in long simulating studies of parameter regimes, and sample sizes. The practical usefulness of the distribution could be demonstrated by the extensive simulation experiments re-creating the real world conditions of health data, including the disease prevalence modeling, the efficacy of disease treatments analysis, biomarker analysis. GB distribution has excellent flexibility to observe distributional properties of complexity like multimodality, heavy tails and fine skewness patterns which are often nonparametrically challenging in current statistical models applied in health research. Extensive goodness-of-fit statistics, model comparison conditions and diagnostic tests are used to establish the improved performance of the distribution compared to the available options.