Informatics and Applications
2021, Volume 15, Issue 2, pp 72-81
CHEBYSHEV-EDGEWORTH EXPANSIONS FOR DISTRIBUTIONS OF GENERALISED HOTELLING-TYPE STATISTICS BASED ON RANDOM SIZE SAMPLES
Abstract
The general transfer theorem for the distribution function of asymptotically normal statistics was generalized on the Hotelling-type statistics case and analog of general transfer theorem for the distribution function of Hotelling-type statistics with random size was proved. It allowed to obtain the Chebyshev-Edgeworth expansion for initial Hotelling-type statistics. The explicit form of the Chebyshev-Edgeworth expansion was obtained for the case when the random sample size distribution is the negative binomial distribution shifted by 1. The limit distribution for this case was F-distribution. The Cornish-Fisher expansion was obtained for the special case of parameter of random sample size. The computational experiment was conducted and graphs were plotted for Chebyshev-Edgeworth expansion illustration.
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[+] About this article
Title
CHEBYSHEV-EDGEWORTH EXPANSIONS FOR DISTRIBUTIONS OF GENERALISED HOTELLING-TYPE STATISTICS BASED ON RANDOM SIZE SAMPLES
Journal
Informatics and Applications
2021, Volume 15, Issue 2, pp 72-81
Cover Date
2021-06-30
DOI
10.14357/19922264210211
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
generalised Chebyshev-Edgeworth expansion; Cornish-Fisher expansion; sample with random size; F-disribution; Hotelling-type statstics
Authors
M. M. Monakhov 
Author Affiliations
Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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