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Informatika i Ee Primeneniya [Informatics and its Applications], 2021, Volume 15, Issue 2, Pages 72–81
DOI: https://doi.org/10.14357/19922264210211
(Mi ia731)
 

Chebyshev–Edgeworth expansions for distributions of generalised Hotelling-type statistics based on random size samples

M. M. Monakhov

Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
References:
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.
Keywords: generalised Chebyshev–Edgeworth expansion, Cornish–Fisher expansion, sample with random size, F-disribution, Hotelling-type statstics.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics
The research was conducted in accordance with the program of the Moscow Center for Fundamental and Applied Mathematics.
Received: 22.06.2020
Document Type: Article
Language: Russian
Citation: M. M. Monakhov, “Chebyshev–Edgeworth expansions for distributions of generalised Hotelling-type statistics based on random size samples”, Inform. Primen., 15:2 (2021), 72–81
Citation in format AMSBIB
\Bibitem{Mon21}
\by M.~M.~Monakhov
\paper Chebyshev--Edgeworth expansions for~distributions of~generalised Hotelling-type statistics based on~random size samples
\jour Inform. Primen.
\yr 2021
\vol 15
\issue 2
\pages 72--81
\mathnet{http://mi.mathnet.ru/ia731}
\crossref{https://doi.org/10.14357/19922264210211}
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