Bringing Closure to the Plotting Position Controversy

In this article, it is explicitly demonstrated that the probability of non exceedance of the mth value in n order ranked events equals m/(n + 1). Consequently, the plotting position in the extreme value analysis should be considered not as an estimate, but to be equal to m/(n + 1), regardless of the parent distribution and the application. The many other suggested plotting formulas and numerical methods to determine them should thus be abandoned. The article is intended to mark the end of the century-long controversial discussion on the plotting positions.

[1]  Clive Anderson,et al.  Estimating Changing Extremes Using Empirical Ranking Methods , 2002 .

[2]  J. R. Wallis,et al.  Estimation of the generalized extreme-value distribution by the method of probability-weighted moments , 1985 .

[3]  R. I. Harris.  Gumbel re-visited - a new look at extreme value statistics applied to wind speeds , 1996 .

[4]  A. Benard,et al.  Het uitzetten van waarnemingen op waarschijnlijkheids‐papier1 , 1953 .

[5]  H. Leon Harter,et al.  Another look at plotting positions , 1984 .

[6]  V. Barnett.  Probability Plotting Methods and Order Statistics , 1975 .

[7]  Irving I. Gringorten,et al.  A plotting rule for extreme probability paper , 1963 .

[8]  M. De,et al.  A new unbiased plotting position formula for Gumbel distribution , 2000 .

[9]  S. L. Guo.  A discussion on unbiased plotting positions for the general extreme value distribution , 1990 .

[10]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[11]  A. Bernard,et al.  The plotting of observations on probability-paper , 1955 .

[12]  C. Cunnane.  Unbiased plotting positions — A review , 1978 .

[13]  L. R. Beard.  Statistical Analysis in Hydrology , 1943 .

[14]  Bradford F. Kimball,et al.  On the Choice of Plotting Positions on Probability Paper , 1960 .

[15]  Nigel W. Arnell,et al.  Unbiased plotting positions for the general extreme value distribution , 1986 .

[16]  Jean Palutikof,et al.  A review of methods to calculate extreme wind speeds , 1999 .

[17]  FRANCIS GALTON,et al.  A Geometric Determination of the Median Value of a System of Normal Variants, from two of its Centiles , 1899, Nature.

[18]  W. Weibull.  A statistical theory of the strength of materials , 1939 .

[19]  J. Angus.  Extreme Value Theory in Engineering , 1990 .

[20]  N. In-na,et al.  An unbiased plotting position formula for the general extreme value distribution , 1989 .

[21]  Allen Hazen,et al.  Storage to be Provided Impounding Reservoirs for Municipal Water Supply , 1913 .

[22]  Eric J. Johnson,et al.  Decisions Under Uncertainty: Psychological, Economic, and Neuroeconomic Explanations of Risk Preference , 2009 .