A simulation based approach to the parameter estimation for the three-parameter gamma distribution

European Journal of Operational Research

Volumn 155, Issue 3, 2004, Pages 675-682

  Pang, Wan Kai ^a   Hou, Shui Hung ^a   Yu, Bosco W T ^a   Li, Ken W K ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b Hong Kong Inst of Voc Education   (Hong Kong)

Author keywords

Adaptive rejection sampling; Continuation method; Gamma distribution; Markov chain Monte Carlo

Indexed keywords

COMPUTER SIMULATION; MARKOV PROCESSES; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; RELIABILITY;

ADAPTIVE REJECTION SAMPLING; CONTINUATION METHOD; GAMMA DISTRIBUTION;

STATISTICAL METHODS;

EID: 0742266966     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(02)00883-4     Document Type: Conference Paper

References (25)

1. Bowman K.O., Shenton L.R. Properties of estimators for the gamma distribution. 1988;Marcel Dekker, New York.
2. Bowman K.O., Shenton L.R., Lam H.K. Simulation and estimation problems associated with the three-parameter gamma distribution. Communications in Statistics-Simulation and Computation. 16:1987;1147-1188.
3. Chen M.H., Shao Q.M., Ibrahim J.G. Monte Carlo Methods in Bayesian Computation. 2000;Springer-Verlag, New York.
4. Cheng R.C.H., Amin N.A.K. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of The Royal Statistical Society Series B. 45:1983;394-403.
5. Cohen A.C., Norgaard N.J. Progressively censored sampling in the three-parameter gamma distribution. Technometrics. 19:1977;333-340.
6. Cohen A.C., Whitten B.J. Modified moment and maximum likelihood estimators for parameters of the three-parameter gamma distribution. Communications in Statistics-Simulation and Computation. 11:1982;197-216.
7. Cohen A.C., Whitten B.J. Modified moment estimation for the three-parameter gamma distribution. Journal of Quality Technology. 18:1986;53-62.
8. Gamerman D. Markov chain Monte Carlo: Stochastic Simulation for Bayesian Inference. 1997;Chapman and Hall, London.
9. Gelfand, A.E., Banerjee, S., 1998. Computing marginal posterior modes using stochastic approximation. Technical Report, # 98-25, Department of Statistics, University of Connecticut.
10. Gelfand A.E., Smith A.F.M. Sampling based approach to calculating marginal densities. Journal of the American Statistical Association. 85:1990;398-409.
11. Geman S., Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Mathematical Intelligence. 6:1984;721-741.
12. Gilks W.R., Best N.G., Tan K.K.C. Adaptive rejection metropolis sampling. Applied Statistics. 44(4):1995;455-472.
13. Gilks W.R., Richardson S., Spiegelhalter D.J. Markov chain Monte Carlo in Practices. 1996;Chapman and Hall, London.
14. Gilks W.R., Wild P. Adaptive rejection sampling for Gibbs sampling. Applied Statistics. 41(2):1992;337-348.
15. Harter H.L., Moore A.H. Maximum-likelihood estimation of the parameters of gamma and Weibull populations from complete and from censored samples. Technometrics. 7:1965;639-643.
16. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 57:1970;97-109.
17. Hirose H. Maximum-likelihood parameter estimation in the three-parameter gamma distribution. Computational Statistics and Data Analysis. 20:1994;343-354.
18. Hirose H. Parameter estimation for the 3-parameter gamma distribution using the continuation method. IEEE Transactions on Reliability. 47(2):1998;188-196.
19. Johnson N.J., Kotz S. Continuous Univariate Distribution-I. 1970;Wiley, New York.
20. Kappenmann R.F. Estimation for the three-parameter Weibull, lognormal and gamma distributions. Computational Statistics and Data Analysis. 3:1985;11-23.
21. Lindley D.V., Smith A.F.M. Bayes estimators for the linear model (with Discussion). Journal of The Royal Statistical Society Series B. 34:1972;1-41.
22. McCool, J.I., 1974. Inferential techniques for Weibull populations. Aerospace Research Laboratories Report ARL TR 74-0180, Wright-Patterson Air Force Base, OH, USA.
23. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equations of state calculations by fast computing machines. Journal Chemical Physics. 21:1953;1087-1091.
24. Tsionas E.G. Bayesian Analysis of finite mixtures of Weibull distributions. Communications in Statistics - Theory and Methods. 31:2002;37-48.
25. Upadhyay S.K., Peshwani M. Full posterior analysis of three parameter lognormal distribution using Gibbs sampler. Journal of Statistical Computation and Simulation. 71:2001;215-230.