Water Engineering Research

Korea Water Resources Association (한국수자원학회)
권호 표지

A COMPARATIVE EVALUATION OF THE ESTIMATORS OF THE 2-PARAMETER GENERALIZED PARETO DISTRIBUTION

  • Singh, V.P. (Louisiana State University) ;
  • Ahmad, M. (Louisiana State University) ;
  • Sherif, M.M. (United Arab Emirates University)
  • Published : 2003.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

Keywords

References

  1. Barrett, J. H., 1992. An extreme value analysis of the flow of Burbage Brook. Stochastic Hydrology and Hydraulics, Vol. 6, pp. 151-165 https://doi.org/10.1007/BF01581447
  2. Baxter, M. A., 1980. Minimum variance unbiased estimation of the parameter of the Pareto distribution. Biometrika, Vol. 27, pp. 133-138 https://doi.org/10.1007/BF01893585
  3. Cook, W. L. and Mumme, D. C., 1981. Estimation of Pareto Parameters by numerical methods. In Statistical Distributions in Scientific Work, C.Taillie et al. (eds.) Vol. 5, pp.127-132
  4. Davison, A. C., 1984a. Modelling excesses over high thresholds, with an application. In Statistical Extremes and Applications, J. Tiago de Oliveira(ed.), pp. 461-482
  5. Davison, A. C., 1984a. A statistical model for contamination due to long-range atmospheric transport of radionuclides. unpublished Ph.D. thesis, Department of Mathematics, Imperial College of Science and Technology, London, England
  6. Davison, A. C. and Smith, R. C., 1990. Models for exceedances over high thresholds. J. R. Statist. Soc. B, Vol. 52, No. 3, pp. 393-442
  7. DuMouchel, W., 1983. Estimating the stable index in order to measure tail thickness. Ann. Statist., Vol. 11, pp. 1019-1036
  8. Hosking, J. R. M. and Wallis, J. R., 1987. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics, Vol. 29, No. 3, pp. 339-349 https://doi.org/10.2307/1269343
  9. Joe, H., 1987. Estimation of quantiles of the maximum of N observations. Biometrika. Vol. 74, pp. 347-354 https://doi.org/10.1093/biomet/74.2.347
  10. Kuczera, G., 1982a. Combining site-specific and regional information: An empirical Bayes approach. Water Resources Research, Vol. 18, No. 2, pp. 306-314
  11. Kuczera, G., 1982b. Robust flood frequency models, Water Resources Research, Vol. 18 No. 2, pp. 315-324
  12. Moharram, S. H., Gosain, A. K. and Kapoor, P. N., 1993. A comparative estimation of the generalized Pareto distribution. Journal of Hydrology, Vol. 150, pp. 169-185
  13. Ochoa, I. D., Bryson, M. C. and Shen, H. W., 1980. On the occurrence and importace of Paretian-tailed distribution in hydrology. Journal of Hydrology, Vol. 48, pp. 53-62 https://doi.org/10.1016/0022-1694(80)90065-7
  14. Pickands, J., 1975. Statistical inference using extreme order statistics. Ann. Statist., Vol. 3, pp. 119-131
  15. Quandt, R. E., 1966. Old and new methods of estimation of the Pareto distribution. Biometrika. Vol. 10, pp. 55-82 https://doi.org/10.1007/BF02613419
  16. Rosbjerg, D., Madsen, H. and Rasmussen, P. F., 1992. Prediction in partial duration series with generalized Pareto-distributed exceedances. Water Resources Research, Vol. 28, No. 11, pp. 3001-3010 https://doi.org/10.1029/92WR01750
  17. Saksena, S. K. and Johnson, A. M., 1984. Best unbiased estimators for the parameters of a two-parameter Pareto distribution. Biometrika, Vol. 31, pp. 77-83 https://doi.org/10.1007/BF01915186
  18. Singh, V. P., 1998. Entropy-Based Parameter Estimation in Hydrology. Kluwer Academic Publishers, Kluwer Academic Publishers
  19. Singh, V. P. and Guo, H., 1995a. Parameter estimation for 2-parameter Pareto distribution by POME. Water Resources Management, Vol. 9, pp. 81-93 https://doi.org/10.1007/BF00872461
  20. Singh, V. P. and Guo, H., 1995b. Parameter estimation for-3 parameter generalized Pareto distribution by the principle of maxmum entropy (POME). Hydrological Sciences Journal, Vol. 40(2), pp. 165-181
  21. Singh, V.P. and Guo, H., 1997. Parameter estimation for 3-parameter generalized Pareto distribution by POME. Stochastic Hydrology and Hydraulics, Vol. 11, pp. 211-227 https://doi.org/10.1007/BF02427916
  22. Singh, V. P. and Rajagopal, A. K., 1986. A new method of parameter estimation for hydrologic frequency analysis. Hydrological Science and Technology, Vol. 2, No. 3, pp. 33-40
  23. Smith, J. A., 1991. Estimating the upper tail of flood frequency distributions. Water Resources Research, Vol. 23, No. 8, pp. 1657-1666
  24. Smith, R.L., 1984. Threshold methods for sample extremes', In Statistical Extremes and Applications (ed. J. Trago de Oliveita), pp. 621-638
  25. Smith, R. L., 1987. Estimating tails of probability distributions. Ann. Statist., Vol. 15, pp. 1174-1207
  26. Van Montfort, M. A. J. V. and Witter, J. V., 1985. Testing exponentialty against generalized Pareto distribution. Journal of Hydrology, Vol. 78, pp. 305-315 https://doi.org/10.1016/0022-1694(85)90108-8
  27. Van Montfort, M. A. J. and Witter, J. W., 1986. The generalized pareto distribution applied to rainfall depths. Hydrological Sciences Journal, Vol. 31, No. 2, pp. 151-162
  28. Van Montfort, M. A. J. and Witter, J. W., 1991. The first and the second e of the extreme value distribution, EVI Stochastic Hydrology and Hydraulics, Vol. 5, pp. 69-76 https://doi.org/10.1007/BF01544179
  29. Wang, Q. J., 1991. The POT model described by the generalized Pareto distribution with Poisson arrival rate. Journal of Hydrology, Vol.129, pp. 263-280 https://doi.org/10.1016/0022-1694(91)90054-L