Stochastic Hydrology and Hydraulics

, Volume 11, Issue 1, pp 51–63 | Cite as

Chowdhury and Stedinger's approximate confidence intervals for design floods for a single site

  • R. Whitley
  • T. V. HromadkaII


A basic problem in hydrology is computing confidence levels for the value of the T-year flood when it is obtained from a Log Pearson III distribution in terms of estimated mean, estimated standard deviation, and estimated skew. In an important paper Chowdhury and Stedinger [1991] suggest a possible formula for approximate confidence levels, involving two functions previously used by Stedinger [1983] and a third function, λ, for which asymptotic estimates are given. This formula is tested [Chowdhury and Stedinger, 1991] by means of simulations, but these simulations assume a distribution for the sample skew which is not, for a single site, the distribution which the sample skew is forced to have by the basic hypothesis which underlies all of the analysis, namely that the maximum discharges have a Log Pearson III distribution. Here we test these approximate formulas for the case of data from a single site by means of simulations in which the sample skew has the distribution which arises when sampling from a Log Pearson III distribution. The formulas are found to be accurate for zero skew but increasingly inaccurate for larger common values of skew. Work in progress indicates that a better choice of λ can improve the accuracy of the formula.


Confidence Interval Waste Water Water Management Water Pollution Stochastic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Advisory Committee on Water Data. 1982: Guidelines for Determining Flood Flow Frequency, Bulletin #17B of the Hydrology Subcommittee, OWDC, US Geological Survey, Reston, VAGoogle Scholar
  2. Bobee, B., et. al. 1993: Towards a systematic approach to comparing distributions used in flood frequency analysis, J. of Hydrology 142, 121–136CrossRefGoogle Scholar
  3. Bobee, B. 1973: Sample error of T-year events computed by fitting a Pearson type 3 distribution, Water Resour. Res. 5, 1264–1270Google Scholar
  4. Bobee, B.; Robitaille, R. 1975: Correction of bias in the estimation of the coefficient of skewness, Water Resour. Res. 11, 851–854Google Scholar
  5. Bobee, B.; Robitaille, R. 1977: The use of the Pearson type 3 and log-Pearson type 3 distributions revisited, Water Resour. Res. 13, 427–443Google Scholar
  6. Bowman, R.; Shenton, L. 1988: Properties of Estimators for the Gamma Distribution, Marcel Dekker, New YorkGoogle Scholar
  7. Burden, R., Faires, J. 1993: Numerical Analysis, 5th ed., PW-Kent, BostonGoogle Scholar
  8. Chowdhury, J.; Stedinger, J. 1991: Confidence intervals for design floods with estimated skew coefficient, ASCE J. Hyd. Eng. 11, 811–831Google Scholar
  9. Cohon, J. et. al. 1988: Estimating Probabilities of Extreme Floods, National Academy Press, Washington D.C.Google Scholar
  10. Devroye, L. 1986: Non-Uniform Random Variable Generation, Springer, New YorkGoogle Scholar
  11. Hardison, C. 1974: Generalized skew coefficients of annual floods in the United States and their application, Water Resour. Res. 10, 745–752Google Scholar
  12. Hu, S. 1987: Determination of confidence intervals for design floods, J. Hydrol. 96, 201–213CrossRefGoogle Scholar
  13. Kirby, W. 1974: Algebraic boundedness of sample statistics, Water Res. Research 10, 220–222Google Scholar
  14. Kite, G. 1975: Confidence intervals for design events, Water Resour. Res. 11, 48–53Google Scholar
  15. Kite, G. 1976: Reply to comments on “Confidence limits for design events”, Water Resour. Res. 12, 826Google Scholar
  16. Lettenmaier, D.; Burges, S. 1980: Correction for bias in estimation of the standard deviation and coefficient of skewness of the log Pearson 3 distribution, Water Resour. Res. 16, 762–766Google Scholar
  17. McCuen, R. 1979: Map skew, J. Water Resour. Plann. Manage., ASCE 105(2) 269–277Google Scholar
  18. Phien, H.; Hsu, L. 1985: Variance of the T-year event in the log-Pearson type 3 distribution, J. Hydrol. 77, 141–158CrossRefGoogle Scholar
  19. Press, W. et. al. 1989: Numerical Recipes in Pascal, Cambridge Univ. Press, New YorkGoogle Scholar
  20. Resnikoff, G.; Lieberman, G. 1957: Tables of the Non-Central t-Distribution, Stanford Univ. Press, CAGoogle Scholar
  21. Stedinger, J. 1980: Fitting log normal distributions to hydrologic data, Water Resour. Res. 16(3) 481–490Google Scholar
  22. Stedinger, J. 1983: Confidence intervals for design events, CEJ. Hyd. Eng. 109, 13–27CrossRefGoogle Scholar
  23. Tasker, G. 1978: Flood frequency analysis with a generalized skew coefficient, Water Resour. Res. 14, 373–376Google Scholar
  24. Tasker, G.; Stedinger, J. 1986: Regional skew with weighted LS regression, ASCE J. Water Resour. Planning Mgmt. 112, 709–722Google Scholar
  25. Whitley, R.; Hromadka II, T. 1986: Computing confidence intervals for floods I, Microsoftware for Engineers 2(3) 138–150Google Scholar
  26. Whitley, R.; Hromadka II, T. 1986: Computing confidence intervals for floods II, Microsoftware for Engineers 2(3) 151–158Google Scholar
  27. Whitley, R.; Hromadka II, T. 1987: Estimating 100-year flood confidence intervals, Adv. Water. Resour. 10, 225–227CrossRefGoogle Scholar
  28. Whitley, R.; Hromadka II, T. 1993: Testing for non-zero skew in maximum discharge runoff data, Water Resour. Res. 29, 531–534CrossRefGoogle Scholar
  29. Wilson, E.; Hilferty, M. 1931: The distribution of chi-square, Proc. Nat. Acad. Sci. U.S.A. 17, 684–688CrossRefGoogle Scholar
  30. World Meteorological Organization. 1989: Operational Hydrology Report 33, Secretariat of the WMO, Geneva, SwitzerlandGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • R. Whitley
    • 1
  • T. V. HromadkaII
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Newport BeachUSA

Personalised recommendations