Water Engineering Research

Korea Water Resources Association (한국수자원학회)
권호 표지

THE STUDY OF PARAMETRIC AND NONPARAMETRIC MIXTURE DENSITY ESTIMATOR FOR FLOOD FREQUENCY ANALYSIS

  • Moon, Young-Il (Department of Civil Engineering , University of Seoul)
  • Published : 2000.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

Magnitude-frequency relationships are used in the design of dams, highway bridges, culverts, water supply systems, and flood control structures. In this paper, possible techniques for analyzing flood frequency at a site are presented. A currently used approach to flood frequency analysis is based on the concept of parametric statistical inference. In this analysis, the assumption is make that the distribution function describing flood data in known. However, such an assumption is not always justified. Even though many people have shown that the nonparametric method provides a better fit to the data than the parometric method and gives more reliable flood estimates. the noparpmetric method implies a small probability in extrapolation beyond the highest observed data in the sample. Therefore, a remedy is presented in this paper by introducing an estimator which mixes parametric and nonparametric density estimate.

Keywords

References

  1. Adamowski, K. (1981). 'Plotting formula for flood frequency.' Water Resources Bulletin, Vol. 17, No, 2, pp. 197-202
  2. Adamowski, K. (1985). 'Nonparametric kernel estimation of flood frequency.' Water Resources Research, Vol. 21, No. 11, pp.1585-1590
  3. Adamowski, K. (1989). 'A Monte Carlo comparison of parametric and nonparametric estimation of flood frequencies.' J. of Hydrology, Vol. 108, pp. 295-308 https://doi.org/10.1016/0022-1694(89)90290-4
  4. Adamowski, K., and Feluch, W. (1990). 'Nonparametric flood-frequency analysis with historical information.' J. of Hydraulic Engineering, Vol. 116, No. 8, pp. 1035-1047
  5. Adamowski, K., and Labatiuk, C. (1987). 'Estimation of flood frequencies by a nonparametric ddensity procedure.' Hydrologic Frequency Modeling, pp. 97-106
  6. Adamowski, K. (1996). 'Nonparametric Estimation of Low-Flow Frequencies.' Journal of Hydraulic Engineering, pp. 46-49 https://doi.org/10.1061/(ASCE)0733-9429(1996)122:1(46)
  7. Bowman, A. W. (1984). 'An alternative method of cross-validation for the smoothing of density estimates.' Biometrika, Vol.71, pp. 353-360 https://doi.org/10.1093/biomet/71.2.353
  8. Breiman, L., Meisel, W. and Purcell, E. (1977). 'Variable kernel estimates of multivariate densities.' Technometrics, Vol. 19, No. 2, pp. 135-144 https://doi.org/10.2307/1268623
  9. Duin, R.P.W. (1976). 'On the choice of smoothing parameters for parzen estimators of probability density functions.' IEEE Trans. Comput. C-25, pp. 1175-1179 https://doi.org/10.1109/TC.1976.1674577
  10. Geisser, S. (1975). 'The predictive sample reuse method with a applications.' J. Amer. Statist Assoc., Vol. 70, pp. 320-328 https://doi.org/10.2307/2285815
  11. Good, I.J., and Gaskins, R.A. (1980). 'Density estimation and bump-hunting by the penalized likelihood method exemplified by scattering and meteorite data.' Journal of the American Statistical Association, Vol. 75, pp. 42-56 https://doi.org/10.2307/2287377
  12. Habbema, J.D.F., Hermans, J. and Broek, V.D. (1974). A stepwise discrimination program using density estimation, In G. Bruckman (Ed.). Physical verlag. Compstat Vienna, pp. 100-110
  13. Hall, P. (1983). 'Large sample optimality of least squares cross-validation in density estimation' Ann. Statist., Vol. 11, pp. 1156-1174
  14. Hall, P., and Marron, J.S. (1987). 'Extent to which least-squares cross-validation minimizes integrated square error in nonparametric density estimation.' Probability Theory Rel. Fields, Vol. 74, pp. 567-581 https://doi.org/10.1007/BF00363516
  15. Lall, U., Moon, Y.I., and Bosworth, K. (1993). 'Kernel flood frequency estimators : bandwidth selection and kernel choice.' Water Resources Research, Vol. 29, No.4. pp. 1003-1015 https://doi.org/10.1029/92WR02466
  16. Moon, Young-Il, Lall, U., and Bosworth, K. (1993). 'A comparison of tail probability estimators.' Journal of Hydrology, Vol. 151, pp. 343-363 https://doi.org/10.1016/0022-1694(93)90242-2
  17. Moon, Young-Il and Lall, U. (1994) 'Kernel quantile function estimator for flood frequency analysis.' Water Resources Research, Vol. 30, No. 11, pp. 3095-3103 https://doi.org/10.1029/94WR01217
  18. Moon, Young-Il and Lall, U. (1995). 'Nonparametric flood frequency analysis by a kernel quantile function estimator.' European Geology Society
  19. Moon, Young-Il. (1996) 'Nonparametric flood frequency analysis' Journal of the Institute of Metropolitan Studies, Vol. 22, No. 1, pp. 231-248
  20. Moon, Young-Il and Cha, Y.I., and Chun, S.Y. (1999). 'The Estimate of Probability Precipitation by Frequency Analysis: Parametric and Nonparametric Methods', Conference Proceedings of Korea Water Resources Association, pp. 117-122
  21. Parzen, E. (1962). 'On estimation of a probability density function and mode.' Ann. Math. Statist., Vol. 33, pp. 1065-1076
  22. Rosenblatt, M. (1956). 'Remarks on some nonparametric estimates of a density function.' Ann. Math. Statist., Vol. 27, pp. 823-837
  23. Ruedmo, M. (1982). 'Empirical choice of histograms and kernel density estimators.' Scand J. Statist., Vol. 9, pp. 65-78
  24. Schuster, E.F., and Yakowitz, S. (1985). 'Parametric/nonparametric mixture density estimation with application to flood-frequency analysis.' Water Resources Bulletin, Vol. 21, No. 5, pp. 797-804 https://doi.org/10.1111/j.1752-1688.1985.tb00173.x
  25. Silverman, B.W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, New York
  26. Stone, M. (1974). 'Cross-validatory choice and assessment of statistical predictions.' J. Roy. Statist. Soc., B 36, pp. 111-147
  27. Stone, M. (1984). 'An asymptotically optimal window selection rule for kernel density estimates' Ann. Statistics, Vol. 12, pp. 1285-1297