Premium
A Note on the Average Probability of Extreme Events
Author(s) -
Appel Charles A.
Publication year - 1968
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr004i006p01359
Subject(s) - mathematics , weibull distribution , limiting , statistics , value (mathematics) , rank (graph theory) , integer (computer science) , position (finance) , probability distribution , combinatorics , expected value , table (database) , computer science , engineering , mechanical engineering , finance , economics , data mining , programming language
In a recent paper, Benson [1967] has shown that the limiting value of the average probability of all floods above the k ‐year flood is equal to 1/2 k ; when the California, Weibull, or Hazen formulas are used to determine plotting positions. The purpose of this article is to show that the limiting value of the average probability is 1/2 k ; for any plotting‐position‐probability formula of the form p = ( m + a ) /( n + b ) where m is the rank with the highest value taken as 1, n is the number of ranked events, and a and b can be selected arbitrarily, except that b cannot be a negative integer. Table 1, adapted from Chow [1964], gives some important plotting‐position formulas.