Browsing by Author "Egbon, Osafu A."

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    Objective Bayesian analysis for the differential entropy of the Gamma distribution
    (2024) Ramos, Eduardo; Egbon, Osafu A.; Ramos, Pedro L.; Rodrigues, Francisco A.; Louzada, Francisco
    The paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.
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    Power-law distribution in pieces: a semi-parametric approach with change point detection
    (2024) Ramos, Pedro L.; Jerez-Lillo, Nixon; Segovia, Francisco A.; Egbon, Osafu A.; Louzada, Francisco
    Piecewise models play a crucial role in statistical analysis as they allow the same pattern to be adjusted over different regions of the data, achieving a higher quality of fit than would be obtained by fitting them all at once. The standard piecewise linear distribution assumes that the hazard rate is constant between each change point. However, this assumption may be unrealistic in many applications. To address this issue, we introduce a piecewise distribution based on the power-law model. The proposed semi-parametric distribution boasts excellent properties and features a non-constant hazard function between change points. We discuss parameter estimates using the maximum likelihood estimators (MLEs), which yield closed-form expressions for the estimators and the Fisher information matrix for both complete and randomly censored data. Since MLEs can be biased for small samples, we derived bias-corrected MLEs that are unbiased up to the second order and also have closed-form expressions. We consider a profiled MLE approach to estimate change points and construct a hypothesis test to determine the number of change points. We apply our proposed model to analyze the survival pattern of monarchs in the Pharaoh dynasties. Our results indicate that the piecewise power-law distribution fits the data well, suggesting that the lifespans of pharaonic monarchs exhibit varied survival patterns.