On interval estimation of the coefficient of variation for the three-parameter Weibull, lognormal and gamma distribution: A simulation-based approach

European Journal of Operational Research

Volumn 164, Issue 2, 2005, Pages 367-377

  Pang, Wan Kai ^a   Leung, Ping Kei ^a   Huang, Wei Kwang ^b   Liu, Wei ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Coefficient of variation; Gamma distribution; Gibbs sampling; Lognormal distribution; Markov chain Monte Carlo; Weibull distribution

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; ERROR ANALYSIS; ESTIMATION; MARKOV PROCESSES; MONTE CARLO METHODS; WEIBULL DISTRIBUTION;

COEFFICIENT OF VARIATIONS; GAMMA DISTRIBUTION; GIBBS SAMPLING; LOGNORMAL DISTRIBUTION; MARKOV CHAIN MONTE CARLO;

OPERATIONS RESEARCH;

EID: 10444273164     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2003.04.005     Document Type: Article

References (59)

1. Ahn, K., 1995. Use of coefficient of variation for uncertainty analysis in fault tree analysis. Reliability Engineering and System Safety 47 (3), 229-230.
2. Aitchison, J., Brown, J.A.C., 1957. The Lognormal Distribution. Cambridge University Press, Cambridge, MA.
3. Belth, J.M., 1996. Price competition in life insurance. Journal of Risk and Insurance 33, 365-379.
4. Bennett, B.M., 1976. On an approximate test for homogeneity of coefficient of variation. In: Ziegler, W.J. (Ed.), Contribution to Applied Statistics. Birkhauser Verlag, Basel, pp. 169-171.
5. Chen, M.H., Shao, Q.M., Ibrahim, J.G., 2000. Monte Carlo Methods in Bayesian Computation. Springer-Verlag, New York.
6. Cohen, A.C., 1951. Estimating parameters of logarithmic normal distributions by maximum likelihood. Journal of the American Statistical Association 46, 206-212.
7. Cohen, A.C., Whitten, B.J., 1980. Estimation in the three-parameter lognormal distribution. Journal of the American Statistical Association 75, 399-404.
8. Cohen, A.C., Whitten, B.J., 1981. Estimation of lognormal distributions. American Journal of Mathematical and Management Sciences 1, 139-153.
9. Cohen, A.C., Whitten, B.J., 1982a. Modified moment and maximum likelihood estimators for parameters of the three-parameter gamma distribution. Communications in Statistics - Simulation and Computation 11, 197-216.
10. Cohen, A.C., Whitten, B.J., 1982b. Modified maximum likelihood and modified moment estimators for the three-parameter Weibull distribution. Communications in Statistics - Theory and Methods 11, 2631-2656.
11. Cohen, A.C., Whitten, B.J., 1986. Modified moment estimation for the three-parameter gamma distribution. Journal of Quality Technology 18 (1), 53-62.
12. Cohen, A.C., Whitten, B.J., Ding, Y., 1984. Modified moment estimation for the three-parameter Weibull distribution. Journal of Quality Technology 16 (3), 159-167.
13. Cohen, A.C., Whitten, B.J., Ding, Y., 1985. Modified moment estimation for the three-parameter lognormal distribution. Journal of Quality Technology 17 (2), 92-99.
14. Dubey, S.D., 1966. Hyper-efficient estimation of the location parameter of the Weibull laws. Naval Research Logistics Quarterly 13, 253-263.
15. Duerst, J., 1956. Yarn evenness measurements should take into account fiber length and surface area. Textile Industry 120, 106-107.
16. Fieller, E.C., 1932. A numerical test of the adequacy of A.T. McKay's approximation. Journal of the Royal Statistical Society 95, 699-702.
17. Fisher, L., 1959. Determinants of risk premium on corporate bonds. Journal of Political Economy 67, 217-237.
18. Gamerman, D., 1997. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman & Hall, London.
19. Geman, S., Geman, D., 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721-741.
20. Gentle, J.E., 1998. Random Number Generation and Monte Carlo Methods. Springer, New York.
21. Gilks, W.R., Best, N.G., Tan, K.K.C., 1995. Adaptive rejection metropolis sampling. Applied Statistics 44 (4), 455-472.
22. Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (Eds.), 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
23. Gilks, W.R., Wild, P., 1992. Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41 (2), 337-348.
24. Giesbrecht, F., Kempthorne, O., 1976. Maximum likelihood estimation in the three-parameter lognormal distribution. Journal of the Royal Statistical Society B 38, 257-264.
25. Gong, J., Li, Y., 1999. Relationship between the estimated Weibull modulus and the coefficient of variation of the measured strength for ceramics. Journal of the American Ceramics Society 82 (2), 449-452.
26. Hamer, A.J., Strachan, J.R., Black, M.M., Ibbotson, C., Elson, R.A., 1995. A new method of comparative bone strength measurement. Journal of Medical Engineering and Technology 19 (1), 1-5.
27. Harter, H.L., Moore, A.H., 1966. Local maximum likelihood estimation of the parameters of three-parameter lognormal populations from complete and censored samples. Journal of the American Statistical Association 61, 842-851.
28. Hastings, W.K., 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109.
29. Hendricks, W.A., Robey, W.K., 1936. The sampling distribution of coefficient of variation. Annals of Mathematical Statistics 7, 129-132.
30. Hill, B.M., 1963. The three-parameter lognormal distribution and Bayesian analysis of a point-source epidemic. Journal of the American Statistical Association 58, 72-84.
31. Hirose, H., 1994. Maximum-likelihood parameter estimation in the three-parameter gamma distribution. Computational Statistics and Data Analysis 20, 343-354.
32. Hirose, H., 1998. Parameter estimation for the 3-parameter gamma distribution using the continuation method. IEEE Transactions on Reliability 47 (2), 188-196.
33. Hoshi, K., Stedinger, J.R., Burges, J., 1984. Estimation of lognormal quantiles: Monte Carlo results and first-order approximation. Journal of Hydrology 71, 1-30.
34. Iglewicz, B., 1967. Some properties of the coefficient of variation. Ph.D. Thesis, Virginia Polytechnic Institute.
35. Iglewicz, B., Myers, R.H., 1970. Comparisons of approximations to the percentage points of the sample coefficient of variation. Technometrics 12, 166-169.
36. IMSL, 1987. IMSL User's Manual Statistical Library, Houston, TX.
37. Johnson, N.L., Kotz, S., 1994. Continuous Univariate Distributions - 1. John Wiley, New York.
38. Kane, V.E., 1978. Some Topics in Multivariate Classifications. Presentation given at SREB Summer Research Conference in Statistics, DeGray State Park Lodge, Arkadelphia, AR.
39. Kane, V.E., 1982. Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution. Communications in Statistics A 11, 1935-1957.
40. Kao, J.H.K., 1959. A graphical estimation of mixed Weibull parameters in life-testing of electron tubes. Technometrics 1, 389-407.
41. Kappenman, R.F., 1985. Estimation for the three-parameter Weibull, lognormal and gamma distributions. Computational Statistics and Data Analysis 3, 11-23.
42. Koopmans, L.H., Owen, D.B., Rosenblatt, J.I., 1964. Confidence intervals for the coefficient of variation for the normal and lognormal distributions. Biometrika 51, 25-32.
43. McCool, J.I., 1974. Inferential techniques for Weibull populations. Aerospace Research Laboratories Report ARL TR 74-0180, Wright-Patterson Air Force Base, OH.
44. McKay, A.T., 1932. Distribution of the coefficient of variation and the extended t-distribution. Journal of Royal Statistical Society 95, 695-698.
45. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E., 1953. Equations of state calculations by fast computing machines. Journal Chemical Physics 21, 1087-1091.
46. Miller, E.G., Karson, M.J., 1977. Testing the equality of two coefficient of variations. In: Proceedings of the Business and Economics Section, Part I. American Statistical Association, pp. 278-283.
47. Pang, W.K., Hou, S.H., Yu, W.T., 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 (3), 675-682.
48. Pearson, E.S., 1932. Comparison of A.T. McKay's approximation with experimental sampling results. Journal of Royal Statistical Society 95, 703-704.
49. Pitman, E.J.G., 1939. Tests of hypotheses concerning location and scale parameters. Biometrika 31, 200-215.
50. Reh, W., Scheffler, B., 1996. Significance tests and confidence intervals for coefficient of variation. Computational Statistics and Data Analysis 22 (4), 449-453.
51. Stedinger, J.R., 1980. Fitting log normal distributions to hydrologic data. Water Resources Research 16, 481-490.
52. Umphrey, G.J., 1983. A comment on McKay's approximation for the coefficient of variation. Communicational Statistics - Simulation and Computing 12 (5), 629-635.
53. Upadhyay, S.K., Peshwani, M., 2001. Full posterior analysis of three parameter lognormal distribution using Gibbs sampler. Journal of Statistical Computation and Simulation 71, 215-230.
54. Wyckoff, J., Bain, L., Engelhardt, M., 1980. Some complete and censored sampling results for the three-parameter Weibull distribution. Journal of Statistical Computation and Simulation 11, 139-151.
55. Yuan, P.T., 1933. On the logarithmic frequency distribution and the semi-logarithmic correlation surface. Annals of Mathematical Statistics 4, 30-74.
56. Zanakis, S.H., 1977. In: Neuts, M.F. (Ed.), Computational Experience with Some Nonlinear Optimization Algorithms in Deriving MLE for the Three-Parameter Weibull Distribution, Algorithmic Methods in Probability. In: TIMS Studies in Management Sciences, vol. 7. North-Holland.
57. Zanakis, S.H., 1979a. Monte Carlo study of some simple estimators of the three-parameter Weibull distribution. Journal of Statistical Computation and Simulation 9, 101-116.
58. Zanakis, S.H., 1979b. Extended pattern search with transformations for the three-parameter Weibull MLE problem. Management Science 25, 1149-1161.
59. Zanakis, S.H., Mann, N.R., 1981. A good simple percentile estimator of the Weibull shape parameter for use when all three parameters are unknown, Unpublished manuscript.