DOI QR코드

DOI QR Code

Estimation for scale parameter of type-I extreme value distribution

  • Choi, Byungjin (Department of Applied Information Statistics, Kyonggi University)
  • 투고 : 2015.02.05
  • 심사 : 2015.03.17
  • 발행 : 2015.03.31

초록

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

키워드

참고문헌

  1. Fiorentino, M. and Gabriele, S. (1984). A correction for the bias of maximum likelihood estimators of Gumbel parameters. Journal of Hydrology, 73, 39-49. https://doi.org/10.1016/0022-1694(84)90031-3
  2. Greenwood, J. A., Landwehr, J. M., Matalas, N. N. and Wallis, J. R. (1979). Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resources Research, 15, 1049-1054. https://doi.org/10.1029/WR015i005p01049
  3. Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68, 813-814. https://doi.org/10.1029/JZ068i003p00813
  4. Gumbel, E. J. (1958). Statistics of extremes, Columbia University Press, New York.
  5. Guo, S. L. (1990). A discussion on unbiased plotting positions for the general extreme value distribution. Journal of Hydrology, 121, 33-44. https://doi.org/10.1016/0022-1694(90)90223-K
  6. Hershfield, M. A. and Kohler, M A. (1960). An empirical appraisal of the Gumbel extreme-value procedure. Journal of Geophysical Research, 65, 1737-1746. https://doi.org/10.1029/JZ065i006p01737
  7. Hosking, J. R. M. and Wallis, J. R. (1995). A comparison of unbiased and plotting-position estimators of L moments. Water Resources Research, 31, 2019-2025. https://doi.org/10.1029/95WR01230
  8. Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). Estimation of the generalized extreme value distribution by the method of probabilities weighted moments. Technometrics, 27, 251-261. https://doi.org/10.1080/00401706.1985.10488049
  9. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous univariate distributions, Volume 2, Second Edition, Wiley, New York.
  10. Jowitt, P. W. (1979). The extreme value type 1 distribution and the principle of maximum entropy. Journal of Hydrology, 42, 23-38. https://doi.org/10.1016/0022-1694(79)90004-0
  11. Kimball, B. F. (1949). An approximation to the sampling variances of an estimated maximum value of given frequency based on fit of doubly exponential distribution of maximum values. The Annals of Mathematical Statistics, 20, 110-113. https://doi.org/10.1214/aoms/1177730097
  12. Lambert, J. and Duan, L. (1994). Evaluating risk of extreme events for univariate-loss functions. Journal of Water Resources Planning and Management, 120, 382-399. https://doi.org/10.1061/(ASCE)0733-9496(1994)120:3(382)
  13. Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979). Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research, 15, 1055-1064. https://doi.org/10.1029/WR015i005p01055
  14. Nam, S. J. and Kang, S. B. (2014). Estimation for the extreme value distribution under progressive Type-I interval censoring. Journal of the Korean Data and Information Science Society, 25, 643-653. https://doi.org/10.7465/jkdi.2014.25.3.643
  15. Rasmussen, P. F. and Gautam, N. (2003). Alternative PWM-estimators of the Gumbel distribution. Journal of Hydrology, 280, 265-271. https://doi.org/10.1016/S0022-1694(03)00241-5
  16. Shannon, C. E. (1948). A mathematical theory of communications. Bell System Technical Journal, 27, 379-423, 623-656. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  17. Stol, P. T. (1971). On the decomposition of the extreme value distribution of daily rainfall depths and the derivation of probabilities of compound events. Journal of Hydrology, 14, 181-196. https://doi.org/10.1016/0022-1694(71)90034-5