Extrapolation of Maxima with Application in Chi Square Test

The paper presents the method of estimating the parameters of extreme statistics distribution by the maximum likelihood method. Knowing the distribution of extreme statistics enables the prediction of the maximum value for periods outside the analysed sample. Such forecasting has many applications. From the analysis of weather phenomena, through floods to financial data. An important part of the work are examples related to the error assessment when making decisions. The examples relate to the selection of the optimal profile when assessing the demand for clothing goods. The method of regression (or classification) trees used in this problem requires at each step the process of selecting the profiles by means of the chi square statistics. For a small number of profiles, one can view all the options and select the highest value for the chi square statistic. However, if the number of possible features increases to several dozen, finding the optimal solution is not possible in a reasonable time. The issue of choosing the optimal profile is equivalent to the problem of set partition.