Bayesian analysis of the inverse generalized gamma distribution using objective priors (original) (raw)
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Survival Analysis for the Inverse Gaussian Distribution: Natural Conjugate and Jeffrey’s Priors
Springer eBooks, 2012
This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters μ and λ and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter (φ = λ/μ) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered.
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A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan [1]. This paper uses Bayes method to estimate the two unknown parameters and the reliability measures of this distribution. The joint posterior distribution of the model parameters cannot be obtained in a convenient form. Therefore, numerical techniques are needed. We apply four Bayesian numerical methods to get random draws from the joint posterior distribution to be used to estimate the model parameters and its reliability measures without deriving the actual joint posterior distribution. It is assumed here that the two model parameters are priori independent random variables with beta and gamma distributions. Two scenarios for the hyperparameters are applied to compare their contributions on the Bayesian inferences. Two real data sets are re-analyzed using the Bayesian techniques applied here. A simulation study is performed to investigate the properties of the methods applied.
2008
Generalized gamma distribution offers a flexible family and many of the important lifetime models are obtained as component models by setting its shape parameters to unity. The flexibility of the generalized gamma model, however, occurs at the cost of its increased complexity. The present paper makes a simulation based Bayesian study to have a thorough comparison of the generalized gamma with its components in situations where the given data appear compatible with this family. Of course, if a component model is recommended the latter inferences are quite easy to deal with. The study has been conducted in two stages. First, the generalized gamma family with a scale and two shape parameters is examined to see if one or both of its shape parameters can be set to unity in order that the component models can be looked upon as possible candidates. Second, a threshold parameter added in to the family selected at the first stage is tested against zero to see if there is any desirability of threshold in the model(s). A real data set is considered for the purpose of illustration. The paper proceeds by checking compatibility of the various component models with the given data set and finally compares the models to select the one that is most pertinent with the data.
A new flexible gamma generalized model with properties, applications and Bayesian approach
2017
1.1.1 CO1.1 A new flexible gamma generalized model with properties, applications and Bayesian approach. Authors: Fábio Prataviera; Gauss M. Cordeiro; Adriano K. Suzuki; Edwin M. M. Ortega. Abstract: We propose a new lifetime model called the odd log-logistic generalized gamma distribution that can be easily interpreted. Some of its special models are discussed. We obtain general mathematical properties of this distribution including the ordinary moments, and quantile functions. We discuss parameter estimation by the maximum likelihood method and a Bayesian approach, where Gibbs algorithms along with metropolis steps are used to obtain the posterior summaries of interest for survival data with right censoring. Further, for different parameter settings, sample sizes and censoring percentages, we perform various simulations and evaluate the behavior of the estimators. The potentiality of the new distribution is proved by means of two real data sets. In fact, the new distribution can pr...
Pesquisa Operacional
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.
Asian Journal of Probability and Statistics, 2022
The Odd Generalized Exponentiated-Inverse Exponential Distribution, a three parameter distribution, is a hybrid of the Generalized Exponential distribution. Each of the parameters were assigned a gamma prior independently resulting to a posterior distribution that is mathematically intractable impossible to obtain marginal posterior distribution for two of the parameters, and a likelihood function that is not known traditionally to R or other statistical software. Resort was made to STAN in order to obtain Bayesian estimates - leveraging on STAN’s provision for user-defined distribution functions. Two datasets were used; remission times (in months) of bladder cancer patients and COVID-19 Survey data in Andalusia, Spain. In the end, the Maximum Likelihood estimates maximized the likelihood more than the Bayesian estimates - though with a slight margin of not more than 0.77. On the other hand, the Bayesian estimates proved to be more stable yielding very negligible standard errors com...
Inverse Generalized Gamma Distribution with it's properties
2020
Abstract: In this paper, we introduce a new life time distribution . This distribution based on the reciprocal of Generalized Gamma (GG) random variable . This new distribution is called the Inverse Generalized Gamma (IGG) Distribution in which some of the inverse distributions are special cases. The important benefit of this distribution is ability to fit skewed data that cannot be fitted accurately by many other ungeneralized life time distributions. This distribution has many applications in pollution data ,engineering ,Biological fields and reliability. Some theoretical properties of the distribution has been studied such as: moments, mode, median and other properties.
An extension of the gamma distribution
Communications in Statistics - Theory and Methods, 2015
The gamma distribution has been widely used in many research areas such as engineering and survival analysis. We present an extension of this distribution, called the Kummer beta gamma distribution, having greater flexibility to model scenarios involving skewed data. We derive analytical expressions for some mathematical quantities. The estimation of parameters is approached by the maximum likelihood method and Bayesian analysis. The likelihood ratio and formal goodness-of-fit tests are used to compare the presented distribution with some of its sub-models and non-nested models. A real data set is used to illustrate the importance of the distribution.