Szacownie kwantyli rozkładów prawdopodobieństwa dla maksymalnych opadów dobowych i krótkich 
ciągów danych obserwacyjnych dla potrzeb projektowania inżynierskiego
[Quantile estimation of probability distributions for maximum daily precipitation and short 
time series of observational data for engineering design]

Ewa Broszkiewicz-Suwaj 
Katedra Zastosowań Matematyki, UPWr, Wrocław


Knowledge of the distribution quantiles of precipitation maximum amounts is required in many 
fields concerning engineering design or hydrological risk assessment. When the number of 
observation years is small, it is not possible to fit the probability distribution function to 
maximum values and to calculate quantiles. This paper presents a procedure for calculating the 
quantiles of the probability distribution of daily precipitation maximums over a year using 
stochastic convergence of distributions. The distribution series of random variables, defined 
based on the cut-off sample with the elimination of the smallest values, made it possible to 
determine the quantiles for times series of order alpha of the distribution. These values were 
approximated by a function from the exponential class and then extrapolated to obtain 
quantiles for the distribution of maxima. The resulting quantile estimates, for short time 
series, were corrected using the kurtosis of the data used for estimation, which leads to a 
very large error reduction.