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Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지 v.21 no.2, 2010년, pp.345 - 354   피인용횟수: 2
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Likelihood ratio in estimating gamma distribution parameters

Rahman, Mezbahur    (Minnesota State University, Mankato, USA and BRAC University   ); Muraduzzaman, S. M.    (Bangladesh Institute of Health Science  );
  • 초록

    The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.


  • 주제어

    Di-gamma function .   grid search method.  

  • 참고문헌 (13)

    1. Cheng, R. C. H. and Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of Royal Statistical Society, Series B, 45, 394-403. 
    2. Cheng, R. C. H. and Iles, T. C. (1987). Corrected maximum likelihood in non-regular problems. Journal of Royal Statistical Society, Series B, 49, 95-101. 
    3. Choi, S. C. and Wette, R. (1969). Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics, 11, 683-690. 
    4. Dang, H. and Weerakkody, G. (2000). Bounds for the maximum likelihood estimates in two-parameter gamma distribution. Journal of Mathematical Analysis and Applications, 245, 1-6. 
    5. Evans, M., Hastings, N. and Peacock, B. (2000). Statistical distributions, Third Edition, John Wiley & Sons, Inc., New York. 
    6. 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. 
    7. Lee, E. T. (1992). Statistical methods for survival data analysis, second edition, John Wiley & Sons, Inc., New York. 
    8. Rahman, M. and Pearson, L. M. (2002). Estimation in two-parameter exponential distributions. Journal of Statistical Computation and Simulation, 70, 371-386. 
    9. Rahman, M., Pearson, L. M. and Martinovic, U. R. (2007). Method of product spacings in the two-parameter gamma distribution. Journal of Statistical Research, 41, 51-58. 
    10. Ranneby, B. (1984). The A spacing method. An estimation method related to the maximum likelihood method. Scandanavian Journal of Statistics, 11, 93-112. 
    11. Shah, A. and Gokhale, D. V. (1993). On Maximum product of spacings (MPS) estimation for Burr XII distributions. Communications in Statistics - Simulation and Computation, 22, 615-641. 
    12. Wilks, D. S. (1990). Maximum likelihood estimation for the gamma distribution using data containing zeros. Journal of Climate, 3, 1495-1501. 
    13. Zhang, J. and Wu, Y. (2005). Likelihood-ratio tests for normality. Compulational Statistics & Data Analysis, 49, 709-721. 
  • 이 논문을 인용한 문헌 (2)

    1. 2012. "" Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지, 23(4): 815~823     
    2. Choi, Ilsu ; Rhee, Sung-Suk 2015. "A transmission distribution estimation for real time Ebola virus disease epidemic model" Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지, 26(1): 161~168     

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