Beta generalized distributions and related exponentiated models: A Bayesian approach

Achcar, Jorge Alberto; Coelho-Barros, Emílio Augusto; Cordeiro, Gauss M.

doi:10.1214/10-bjps133

Cited by 12 publications

(8 citation statements)

References 26 publications

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“…A reparameterization method from the Birnbaum-Saunders lifetime model was proposed by Ahmed et al [ 33 ]. Later, Achcar et al [ 34 ] considered a reparameterization from certain skewed models. A reparameterization method may be applied in terms of the log-likelihood functions considering data x = ( x 1 , x 2 ,…, x n ) from the models described earlier which are given in the following.…”

Section: Methods Of Goodness Of Fitmentioning

confidence: 99%

Inferential Statistics from Black Hispanic Breast Cancer Survival Data

Khan

Saxena

Ross³

et al. 2014

The Scientific World Journal

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In this paper we test the statistical probability models for breast cancer survival data for race and ethnicity. Data was collected from breast cancer patients diagnosed in United States during the years 1973–2009. We selected a stratified random sample of Black Hispanic female patients from the Surveillance Epidemiology and End Results (SEER) database to derive the statistical probability models. We used three common model building criteria which include Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) to measure the goodness of fit tests and it was found that Black Hispanic female patients survival data better fit the exponentiated exponential probability model. A novel Bayesian method was used to derive the posterior density function for the model parameters as well as to derive the predictive inference for future response. We specifically focused on Black Hispanic race. Markov Chain Monte Carlo (MCMC) method was used for obtaining the summary results of posterior parameters. Additionally, we reported predictive intervals for future survival times. These findings would be of great significance in treatment planning and healthcare resource allocation.

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Section: Methods Of Goodness Of Fitmentioning

confidence: 99%

Inferential Statistics from Black Hispanic Breast Cancer Survival Data

Khan

Saxena

Ross³

et al. 2014

The Scientific World Journal

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“…Figure 1 presents pdf curves of BW, BF, BKw, and BLL for several parameters values. Due to the inclusion of shape parameters ( a and b ), these distributions are more flexible than their baselines and are candidates for modeling positive real data sets 47–49 …”

Section: The Beta‐g Distribution Familymentioning

confidence: 99%

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Vasconcelos

Cintra

Nascimento

2021

Math Methods in App Sciences

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In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fréchet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T 2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

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“…Later, Achcar et al (2013) considered a reparameterization some skewed models. One may utilize a reparameterization method by considering the log-likelihood functions from the EWM that is described as follows: Assume r 1 =log(a); r 2 =log(β); and r 3 =log(λ).…”

Section: Measures Of Goodness Of Fitmentioning

confidence: 99%