Abstract
In this paper, the more convenient estimators of both parameters of the gamma distribution are proposed by using its characterization, and shown to be more efficient than the maximum likelihood estimator and the moment estimator for small samples. Furthermore, the distribution of the square of the sample coefficient of variation is obtained by computer simulation for some various values of the parameters and sample size, and thus the simulated confidence interval of its shape parameter is established.
Similar content being viewed by others
References
Bai, J., Jakeman, A. J. and McAleer, M. (1991). A new approach to maximum likelihood estimation of the three-parameter gamma and Weibull distributions, Austral. J. Statist., 33, 397–410.
Bowman, K. O. and Shenton, L. R. (1988). Properties of estimators for the gamma distribution, Marcel Dekker, New York.
Bowman, K. O., Shenton, L. R. and Lam, H. K. (1987). Simulation and estimation problems associated with the three-parameter gamma distribution, Comm. Statist. Simulation Comput., 16, 1147–1188.
Cohen, A. C. and Norgaard, N. J. (1977). Progressively censored sampling in the three-parameter gamma distribution, Technometrics, 19, 333–340.
Cohen, A. C. and Whitten, B. J. (1982). Modified moment and maximum likelihood estimators for parameters of the three-parameter gamma distribution, Comm. Statist. Simulation. Comput., 11, 197–216.
Greenwood, J. A. and Durand, D. (1960). Aids for fitting the gamma distribution by maximum likelihood, Technometrics, 2, 55–65.
Harter, H. L. and Moore, A. H. (1965). Maximum-likelihood estimation of the parameters of the gamma and Weibull populations from complete and from censored samples, Technometrics, 7, 639–643.
Hu, C. Y. (1990). On signal to noise ratio statistics, Ph. D. Thesis, Institute of Statistics, National Tsing Hua University, Taiwan.
Hwang, T. Y. (2000). On the inference of parameters of gamma distribution, Tech. Report, 89–2118-M-007–014, National Science Council, Taiwan.
Hwang, T. Y. and Hu, C. Y. (1999). On a characterization of the gamma distribution: The independence of the sample mean and the sample coefficient of variation, Ann. Inst. Statist. Math., 51, 749–753.
Hwang, T. Y. and Hu, C. Y. (2000). On some characterizations of population distribution, Taiwanese J. Math., 4(3), 427–437.
Hwang, T. Y. and Lin, Y. K. (2000). On the distribution of the sample heterogeneity of molecular polymer, Tamsui Oxford Journal of Mathematical Sciences, 16(2), 133–149.
Johnson, N. J. and Kotz, S. (1970). Continuous Univariate Distributions-1, Wiley, New York.
Thom, H. C. S. (1958). A note on the gamma distribution, Washington, Monthly Weather Review, 86(4), 117–121, Office of Climatology, U. S. Weather, Washington D. C.
Author information
Authors and Affiliations
About this article
Cite this article
Hwang, TY., Huang, PH. On New Moment Estimation of Parameters of the Gamma Distribution Using its Characterization. Annals of the Institute of Statistical Mathematics 54, 840–847 (2002). https://doi.org/10.1023/A:1022471620446
Issue Date:
DOI: https://doi.org/10.1023/A:1022471620446