Abstract
In this paper, the confidence intervals for the generalized gamma distribution parameters are derived based on the Bayesian approach using the informative and non-informative priors and the classical approach, via the Asymptotic Maximum likelihood estimation, based on the generalized order statistics. For measuring the performance of the Bayesian approach comparing to the classical approach, the confidence intervals of the unknown parameters have been studied, via Monte Carlo simulations and some real data. The simulation results indicated that the confidence intervals based on the Bayesian approach compete and outperform those based on the classical approach.
Highlights
A random variable X is said to have generalized gamma distribution (GGD) if its probability density function (PDF) has the form: f (x;, ) ( ) x 1 exp (x / ), x 0, 0. [1]( ) is the gamma function, and are the shape, scale and index parameters respectively
In this paper, the Bayesian inference using the informative and non-informative priors are derived based on the generalized order statistics (GOS), that introduced by Kamps (1995) as a unified approach to several models of ordered random variables such as ordinary order statistics, type-II censored order statistics, type-II progressive censored order statistics, upper record values and sequential order statistics
To assess the performance of the confidence intervals based on the Bayesian approach comparing to those based on the asymptotic maximum likelihood estimation approach, Monte Carlo simulations, are carried out in terms of the following criteria: i) Covering percentage (CP), which is defined as the fraction of times the confidence interval covers the true value of the parameter in repeated sampling. ii) The mean length of intervals (MLI). iii) The standard error of the covering percentage (SDE), which is defined for the nominal level (1 )100% by SDE ( ˆ )
Summary
A random variable X is said to have generalized gamma distribution (GGD) if its probability density function (PDF) has the form: f Bayesian Inference on the Generalized Gamma Distribution et al (2008), Geng and Yuhlong (2009). Bayesian and non-Bayesian estimation related to the GGD based on the generalized order statistics (GOS) were not addressed in the literature. In this paper, the Bayesian inference using the informative and non-informative priors are derived based on the GOS, that introduced by Kamps (1995) as a unified approach to several models of ordered random variables such as ordinary order statistics, type-II censored order statistics, type-II progressive censored order statistics, upper record values and sequential order statistics.
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