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Keywords:

  • maxima;
  • Gumbel distribution;
  • Generalized Extreme–Value distribution;
  • partial duration series;
  • Poisson process;
  • seasonal variation;
  • maximum likelihood;
  • best linear unbiased estimates;
  • probability–weighted moments;
  • precipitation;
  • temperature;
  • snow cover

Climatology is an area with many applications of extreme–value theory. In applications to climatic data it is necessary to consider the distribution ol extremes for dependent random variables and to make allowance for non–stationarity (seasonal variation). It is shown that also for such data the classical limiting distributions for normalized maxima of independent and identically distributed random variables remain useful candidates to describe the distribution of the largest value in a year.

Parameter estimation of extreme–value distributions is briefly reviewed. Attention is paid to variance–reduction of quantile estimates by making use of more observations than just the annual maxima. Three examples of applications deal with topics like the estimation of large quantiles by combining information from several records in a region, shifts in the distribution of maxima due to changes in measurement practices, and the use of covariates.