Wybrane testy zgodności dotyczące rozkładów statystyk ekstremalnych i ich zastosowanie w analizach finansowych
Selected tests of goodness of extreme distributions and their application in financial analyses

Summary/Abstract: Minimum and maximum statistics are used in the financial analyses, insurance, meteorology and quality control. The appearance of untypical events causes large financial losses. The sizes of these losses determine the limiting distribution of extreme statistics, which may be the Fréchet, Weibull or Gumbel distribution. The verification of the hypothe-sis that the distribution function belongs to the Gumbel distribution is based on the good-ness-of-fit tests. There are two groups among the tests. Some of the tests require a random sample consisting of the minimum or maximum values, other are based on order statistics, which exceed a prespecified level, called a threshold. This paper presents the results of ana-lyzes of the selected tests and the example of their application to the verification of the sta-tistical hypotheses about the form of the distribution of logarithmic returns of the selected indexes.

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