Simulation of distribution of the maximum of the Chentsov field on ‘steps’

Abstract

The paper extends the results obtained by Paranyap, Park, Klesov and Kruglova. A method of finding the distribution of the maximum of a Chentsov field restriction on a polyline is suggested. To do this, it was proposed to simulate a random process that corresponds to the restriction. The suggested algorithm has high computational efficiency which is crucial due to a large number of points of division of the process trajectory. The selection of the distributions of extreme functionals from the field was performed by means of the statistical programming language R. The Weibull distribution was chosen as the most suitable distribution, which was confirmed by the Kolmogorov criterion, as well as by Q–Q and P–P diagrams. Ref. 10, fig. 7.

Keywords

• Chentsov field
• percolation
• Gaussian process
• maximum distribution
• modelling
• language R