  The paper presents improved mathematical models and methods for statistical
regularities in the behavior of some important characteristics of
precipitation: duration of a wet period, maximum daily and total precipitation
volumes within a such period. The asymptotic approximations are deduced using
limit theorems for statistics constructed from samples with random sizes having
the generalized negative binomial (GNB) distribution. It demonstrates excellent
concordance with the empirical distribution of the duration of wet periods
measured in days. The asymptotic distribution of the maximum daily
precipitation volume within a wet period turns out to be a tempered scale
mixture of the gamma distribution with the scale factor having the Weibull
distribution, whereas the asymptotic approximation to the total precipitation
volume for a wet period turns out to be the generalized gamma (GG)
distribution. Two approaches to the definition of abnormally extremal
precipitation are presented. The first approach is based on an excess of a
certain quantile of the asymptotic distribution of the maximum daily
precipitation. The second approach is based on the GG model for the total
precipitation volume. The corresponding statistical test is compared with a
previously proposed one based on tha classical gamma distribution using real
precipitation data.
