Informatics and Applications
2020, Volume 14, Issue 4, pp 3336
ON THE DISTRIBUTION OF THE RATIO OF THE SUM OF SAMPLE ELEMENTS EXCEEDING A THRESHOLD TO THE TOTAL SUM OF SAMPLE ELEMENTS. II
Abstract
The problem of description of the distribution of the ratio of the sum of sample elements exceeding a threshold to the total sum of sample elements is considered. Unlike other versions of this problem in which the number of summed extreme order statistics and the threshold are fixed, here the specified threshold can be exceeded by an unpredictable number of sample elements. The situation is considered where the threshold infinitely increases as the sample size grows. It is demonstrated that in this case, the distribution of the ratio mentioned above can be approximated by the compound Poisson distribution in which the compounding law is the generalized Pareto distribution.
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[+] About this article
Title
ON THE DISTRIBUTION OF THE RATIO OF THE SUM OF SAMPLE ELEMENTS EXCEEDING A THRESHOLD TO THE TOTAL SUM OF SAMPLE ELEMENTS. II
Journal
Informatics and Applications
2020, Volume 14, Issue 4, pp 3336
Cover Date
20201230
DOI
10.14357/19922264200405
Print ISSN
19922264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
sum of independent random variables; random sum; binomial distribution; Poisson approximation; extreme order statistic; BalkemaDe Haan  Pickands theorem; generalized Pareto distribution; compound Poisson distribution
Authors
V. Yu. Korolev ,
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP1, Leninskie Gory, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
