Browse > Article
http://dx.doi.org/10.5351/CKSS.2007.14.1.255

Bayesian Parameter Estimation of the Four-Parameter Gamma Distribution  

Oh, Mi-Ra (Department of Statistics, Chonnam National University)
Kim, Kyung-Sook (Department of Statistics, Chonnam National University)
Cho, Wan-Hyun (Department of Statistics, Chonnam National University)
Son, Young-Sook (Department of Statistics, Chonnam National University)
Publication Information
Communications for Statistical Applications and Methods / v.14, no.1, 2007 , pp. 255-266 More about this Journal
Abstract
A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.
Keywords
Four-parameter gamma distribution; noninformative prior; Gibbs sampling; adaptive rejection sampling; adaptive rejection Metropolis sampling;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Roberts, G. O. and Smith, A. F. M. (1994). Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms. Stochastic Processes and their Applications, 49, 207-216   DOI   ScienceOn
2 Hager, H. W. and Bain, L. J. (1970). Inferential procedures for the generalized gamma distribution. Journal of the American Statistical Association, 65, 1601-1609   DOI
3 Hager, H. W., Bain, L. J. and Antle, C. E. (1971). Reliability estimation for the generalized gamma distribution and robustness of the Weibull model. Technometrics, 13, 547-557   DOI
4 Harter, H. L. (1967). Maximum-likelihood estimation of the parameters of a four-parameter generalized gamma population from complete and censored samples. Technometrics, 9, 159-165   DOI   ScienceOn
5 Harter, H. L. and Moore, A. H. (1965). Maximum-likelihood estimation of the parameters of gamma and Weibull populations from complete and from censored samples. Technometrics, 7, 639-643   DOI
6 Johnson, N. L. and Kotz, S. (1970). Distributions in Statistics: Continuous Univariate Distributions-1. John Wiley & Sons, New York
7 Lawless, J. F. (1980). Inference in the generalized gamma and log gamma distributions. Technometrics, 22, 409-419   DOI
8 Parr, V. B. and Webster, J. T. (1965). A method for the discriminating between failure density functions used in reliability predictions. Technometrics, 7, 1-10   DOI
9 Pang, W. K., Hou, S. H., Yu, B. W. T. and Li, K. W. K. (2004). A simulation based approach to the parameter estimation for the three-parameter gamma distribution. European Journal of Operational Research, 155, 675-682   DOI   ScienceOn
10 Son, Y, Sand Oh, M. (2006). Bayesian estimation of the two-parameter gamma distribution. Communications in Statistics-Simulation and Computation, 35, 285-293   DOI   ScienceOn
11 Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika, 61, 539-544   DOI   ScienceOn
12 Abramowitz, M. and Stegun, I. A. (1972). Polygamma Functions. Handbook of Mathematical Functions with Formulas, Graph, and Mathematical Tables, 9th printing, Dover, New York
13 Bowman, K. O. and Shenton, L. R. (1988). Properties of Estimators for the Gamma Distribution. Marcel Dekker, New York
14 Cohen, A .C. and Norgaard, N. J. (1977). Progressively censored sampling in the three-parameter gamma distribution. Technometrics, 19,333-340   DOI
15 Cohen, A. C. and Whitten, B. J. (1982). Modified moment and maximum likelihood estimators for parameters of the three-parameter gamma distribution. Communications in Statistics-Simulation and Computation. 11, 197-216   DOI   ScienceOn
16 Gilks, W. R., Best, N. G. and Tan, K. K. C. (1995). Adaptive rejection Metropolis sampling within Gibbs sampling. Applied Statistics, 44, 455-472   DOI   ScienceOn
17 Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337-348   DOI   ScienceOn
18 Stacy, E. W. (1973). Quasimaximum likelihood estimators for two-parameter gamma distributions. IBM Journal of Research and Development, 17, 115-124   DOI
19 Greenwood, J. A. and Durand, D. (1960). Aids for fitting the gamma distribution by maximum likelihood. Technometrics, 2, 55-65   DOI
20 Ritter, C. and Tanner, M. A. (1992). Facilitating the Gibbs sampler: the Gibbs stopper and the griddy-Gibbs sampler. Journal of the American Statistical Association, 87, 861-868   DOI
21 Stacy, E. W. and Mihram, G. A. (1965). Parameter estimation for a generalized gamma distribution. Technometrics, 7, 349-358   DOI
22 Tsionas, E. G. (2001). Exact inference in four-parameter generalized gamma distribution. Communications in Statistics-Theory and Methods, 30, 747-756   DOI   ScienceOn
23 The MathWorks Inc. (2002). MATLAB/Statistics Toolbox, Version 6.5. Natick, MA
24 Thom, H. C. S. (1958). A note on the gamma distribution. Monthly Weather Review, 86,117-122   DOI
25 Cohen, A. C. and Whitten, B. J. (1986). Modified moment estimation for the three-parameter gamma distribution. Journal of Quality Technology, 18, 53-62   DOI
26 Ripley, B. D. (1988). Stochastic Simulation. John Wiley & Sons, New York