Informatics and Applications
2016, Volume 10, Issue 2, pp 84-91
GENERALIZED CORNISH-FISHER EXPANSIONS FOR DISTRIBUTIONS OF STATISTICS BASED ON SAMPLES OF RANDOM SIZE
- A. S. Markov
- M. M. Monakhov
- V. V. Ulyanov
Abstract
Generalized Cornish-Fisher expansions are constructed for quantiles of sample mean for a sample of random size in terms of quantiles for the Laplace distribution and Student's t-test. In recent years, the interest in Cornish-Fisher expansions grew significantly in the context of research on risk management. The widespread risk measure Value at Risk, or VaR, is, in fact, the quantile of the loss function. The authors use the general transfer theorem that makes it possible to obtain asymptotic expansions for the distribution functions of statistics based on samples of random size by asymptotic expansions for the distribution function of the random sample size and asymptotic expansions for the distribution functions of statistics based on nonrandom samples. A computational experiment was performed to illustrate the obtained Cornish-Fisher expansions.
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[+] About this article
Title
GENERALIZED CORNISH-FISHER EXPANSIONS FOR DISTRIBUTIONS OF STATISTICS BASED ON SAMPLES OF RANDOM SIZE
Journal
Informatics and Applications
2016, Volume 10, Issue 2, pp 84-91
Cover Date
2016-05-30
DOI
10.14357/19922264160210
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
quantiles; generalized Cornish-Fisher expansions; random size sample; Laplace distribution
Authors
A. S. Markov  , M. M. Monakhov , and V. V. Ulyanov
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
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