Abstract
Abstract A practical solution of the extreme value (largest value) distribution known as the most rational distribution formula for frequency analysis of the annual maximum hydrologic amount has been proposed in this paper. Practically, there are two types in this distribution as follows;
F (x) =exp (-e-ξ)
ξ=α(x-x0): Gumbel Distribution
ξ=αlogx+b/x0+b: Type A of Log-extreme Value Distribution
in which α, xo, and b are constants.
The solutions by moment of this distribution were already proposed by Gumbel and the author, but the results by those methods were not so good in fitness to hydrologic data. In hydrologic statistics, in order to avoid such a fault, there is a trend to notice an expedient method using the concept of plotting position.
In this paper, the concept of plotting value proposed by the author has been used. Now, the plotting value y is the linear reduced variate of actual variate x, and it is determined to minimize the estimation error of parameter. In this paper, the character, in which the sample moments of plotting value y are corresponding to those of actual variate x, has been utilized.
The method of practical analysis has been shown as the function of sample size n, and some practical tables and diagrams have been prepared. The usefullness of this proposed method were recognized by applying to the actual data of precipitation in many observatories in Japan.
