754
Views
51
CrossRef citations to date
0
Altmetric
EXTREME VALUE ANALYSIS AND ORDER STATISTICS

Bringing Closure to the Plotting Position Controversy

Pages 460-467 | Received 27 Oct 2006, Accepted 27 Apr 2007, Published online: 30 Jan 2008

References

  • Anon ( 1923 ). Flow in California streams . Calif. Dep. Public. Works, Div. Eng. Irrig. Bull 5 .
  • Anon ( 2006 ). Engineering Statistics Handbook . NIST/SEMATECH e-Handbook of Statistical Methods, 2006, http://www.itl.nist.gov/div898/handbook .
  • Arnell , N. V. , Beran , M. , Hosking , J. R. M. ( 1986 ). Unbiased plotting position for the general extreme value distribution . J. Hydrol. 86 : 59 – 69 .
  • Barnett , V. ( 1975 ). Probability plotting methods and order statistics . Appl. Statist. 24 : 95 – 108 .
  • Beard , L. R. ( 1943 ). Statistical analysis in hydrology . Trans. Am. Soc. Civ. Eng. 108 : 1110 – 1160 .
  • Benard , A. , Bos-Levenbach , E. C. ( 1953 ). The plotting of observations on probability paper . Statistica 7 : 163 – 173 .
  • Castillo , E. ( 1988 ). Extreme Value Theory in Engineering . San Diego : Academic Press .
  • Coles , S. ( 2001 ). An Introduction to Statistical Modeling of Extreme Values . Amsterdam : Springer .
  • Cunnane , C. ( 1978 ). Unbiased plotting positions – a review . J. Hydrol. 37 : 205 – 222 .
  • De , M. ( 2000 ). A new unbiased plotting position formula for the Gumbel distribution . Stoch. Environ. Res. Risk Assess. 14 : 1 – 7 .
  • Folland , C. , Anderson , C. ( 2002 ). Estimating changing extremes using empirical ranking methods . J. Climate 15 : 2954 – 2960 .
  • Galton , F. (1899). A geometric determination of the median of a system of normal variants from two sites of its centiles. Nature 61:102–104.
  • Gringorten , I. I. ( 1963 ). A plotting rule for extreme probability paper . J. Geophys. Res. 68 : 813 – 814 .
  • Gumbel , E. J. ( 1939 ). La probabilite des hypotheses . Compt. Rend. Acad. Sci. (Paris) 209 : 645 – 647 .
  • Gumbel , E. J. ( 1958 ). Statistics of Extremes . New York : Columbia University Press .
  • Guo , S. L. ( 1990 ). A discussion on unbiased plotting positions for the general extreme value distribution . J. Hydrol. 121 : 33 – 44 .
  • Harris , R. I. ( 1996 ). Gumbel re-visited – a new look at extreme value statistics applied to wind speeds . J. Wind Eng. Ind. Aerodyn. 59 : 1 – 22 .
  • Harter , H. L. ( 1984 ). Another look at plotting positions . Commun. Statist.—Theor. Meth. 13 : 1613 – 1633 .
  • Hazen , A. ( 1914 ). Storage to be provided in impounding reservoirs for municipal water supply . Trans. Am. Soc. Civ. Eng. 77 : 1547 – 1550 .
  • Hosking , J. R. , Wallis , J. R. , Wood , E. F. ( 1985 ). Estimation of the generalized extreme-value distribution by the method of probability weighted moments . Technometrics 27 : 251 – 261 .
  • In-na , N. , Nguyen , V. ( 1989 ). An unbiased plotting position formula for the general extreme value distribution . J. Hydrol. 106 : 193 – 209 .
  • Jones , D. A. ( 1997 ). Plotting positions via the maximum-likelihood for a non-standard situation . Hydrol. Earth Syst. Sci. 1 : 357 – 366 .
  • Johnson , L. G. ( 1951 ). The median ranks of sample values in the population with application to certain fatigue studies . Ind. Math. 2 : 1 – 9 .
  • Jordaan , I. ( 2005 ). Decisions under Uncertainty . Cambridge : Cambridge University Press .
  • Kimball , B. F. ( 1960 ). On the choice of plotting positions on probability paper . J. Amer. Statist. Assoc. 55 : 546 – 560 .
  • Langbein , W. B. ( 1960 ). Plotting positions in frequency analysis . U. S. Geol. Surv. Water Supply Pap. 1543-A : 48 – 51 .
  • Palutikof , J. P. , Brabson , B. B. , Lister , D. H. , Adcock , S. T. ( 1999 ). A review of methods to calculate extreme wind speeds . Meteorol. Appl. 6 : 119 – 132 .
  • Weibull , W. ( 1939 ). A statistical theory of strength of materials . Ing. Vet. Ak. Handl. (Stockholm) 151 : 45 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.