Browsing by Author "Rodrigues, Francisco A."

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    POWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS
    (2023) Ramos, Pedro Luiz; Rodrigues, Francisco A.; Ramos, Eduardo; Dey, Dipak K.; Louzada, Francisco
    Using objective priors in Bayesian applications has become a common way of analyzing data without using subjective information. Formal rules are usually used to obtain these prior distributions, and the data provide the dominant infor-mation in the posterior distribution. However, these priors are typically improper, and may lead to an improper posterior. Here, for a general family of distribu-tions, we show that the objective priors obtained for the parameters either follow a power law distribution, or exhibit asymptotic power law behavior. As a result, we observe that the exponents of the model are between 0.5 and 1. Understand-ing this behavior allows us to use the exponent of the power law directly to verify whether such priors lead to proper or improper posteriors. The general family of distributions we consider includes essential models such as the exponential, gamma, Weibull, Nakagami-m, half-normal, Rayleigh, Erlang, and Maxwell Boltzmann dis-tributions, among others. In summary, we show that understanding the mechanisms that describe the shape of a prior provides essential information that can be used to understand the properties of posterior distributions.
  • No Thumbnail Available
    Item
    Sampling with censored data: a practical guide
    (2024) Ramos, Pedro L.; Guzman, Daniel C. F.; Mota, Alex L.; Saavedra, Daniel A.; Rodrigues, Francisco A.; Louzada, Francisco
    In this review, we present a simple guide for researchers to obtain pseudo-random samples with censored data. We focus our attention on the most common types of censored data, such as type I, type II, and random censoring. We discussed the necessary steps to sample pseudo-random values from long-term survival models where an additional cure fraction is informed. For illustrative purposes, these techniques are applied in the Weibull distribution. The algorithms and codes in R are presented, enabling the reproducibility of our study. Finally, we developed an R package that encapsulates these methodologies, providing researchers with practical tools for implementation.