Stochastic Limits for Maximum Possible Amount of Precipitation

Abstract

The methods hitherto in use may be considered to have no reasonable theoretical background and by some examples we proved that the goodness of fit by any of them is not satisfactory in general.
We proposed a new method which consists of the following steps: 1) We estimate a “ normalizing transformation curve ” by which the empirical distribution function of logarithms of observed variates is transformed to a normal one.2) We extrapolate the normalizing transformation curve to not yet experienced region by utilizing the Fisher-Tippett s limiting distribution function for the largest member of a sample.3) By a two-sample theory we give the stochastic limits for the transformed normal variates corresponding to any given probability.4) Lastly we transform the stochastic limits inversely to that for amount of precipitation.
The above method is based on the stationarity and randomness of observed time series; if it is not stationary we should use the data in the ‘ recent stationary period ’, and if it has any autocorrelation, firstly we should estimate the type of the stochastic process and then we use a generalized formula for the stochastic limits according to the type.