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) |
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 |