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.