Methodology of the Extreme Value Theory Application for Data Analysis

Михайло Захарович Згуровський, Петро Іванович Бідюк, Світлана Віталіївна Трухан


Background. To solve the problems of modeling and forecasting on the basis of large datasets (including singular ones) in conditions of uncertainty it is necessary to develop integrated information decision support systems (DSS). A methodology is proposed for application of extreme value theory for statistical models development and DSS on their basis.

Objective. The goal of the study is in application of the extreme value theory for analysis and estimation of model parameters on the basis of random samples. It is necessary to develop an effective methodology for analysis of pseudorandom sequences and estimation of unknown model parameters; to present examples of analysis using extreme value theory and software developed.

Methods. To solve the problems stated the following approaches were used: pseudorandom sequences generating procedures; probabilistic distributions of the extreme value theory, and methods for estimating unknown model parameters. A multistep methodology is proposed for extreme values processing and DSS is developed for analysis and modeling of pseudorandom sequences.

Results. Using the DSS developed and generated statistical data as well as proposed methodology the procedure was developed for extreme values analysis. The procedure is to be used for estimating of forecasting models for the process of various origin. A comparative analysis of parameter characteristics for GEV-distributions was performed.

Conclusions. Using the instrumentation developed it was shown that the proposed methodology for processing extreme values is convenient for analysis of singular datasets. This is substantiated with the high quality approximation of theoretical probability density by empirical curve. A comparison of model parameters estimation results showed that the estimates converge faster when parameters of form and scale are defined more exactly.


Extreme value theory; Maximum likelihood estimator; Simulation and modeling; Decision support system


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