Abstract:
We investigate the problem of characterizing the distribution of
independent identically distributed random variables
X1,…,Xm (general distribution) by the distribution of
linear statistics and statistics of maximum with positive
coefficients. Necessary and sufficient conditions are found under
which such a characterization takes place.
Keywords:
characterization of distributions by the distributions of statistics, linear statistics, statistics of maximum.
Citation:
D. V. Belomestny, “Reconstruction of the general distribution by the distribution of some
statistics”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 3–20; Theory Probab. Appl., 49:1 (2005), 1–15
\Bibitem{Bel04}
\by D.~V.~Belomestny
\paper Reconstruction of the general distribution by the distribution of some
statistics
\jour Teor. Veroyatnost. i Primenen.
\yr 2004
\vol 49
\issue 1
\pages 3--20
\mathnet{http://mi.mathnet.ru/tvp233}
\crossref{https://doi.org/10.4213/tvp233}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141327}
\zmath{https://zbmath.org/?q=an:1089.62006}
\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 1--15
\crossref{https://doi.org/10.1137/S0040585X9798083X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000228185300001}
Linking options:
https://www.mathnet.ru/eng/tvp233
https://doi.org/10.4213/tvp233
https://www.mathnet.ru/eng/tvp/v49/i1/p3
This publication is cited in the following 3 articles:
D. V. Belomestny, A. V. Prokhorov, “Stability of characterization the independence of random variables by the independence of the linear statistics”, Theory Probab. Appl., 59:4 (2015), 672–677
Schlager W., Warrlich G., “Record of sea-level fall in tropical carbonates”, Basin Research, 21:2 (2009), 209–224
Ursula U. Müller, Anton Schick, Wolfgang Wefelmeyer, Statistical Models and Methods for Biomedical and Technical Systems, 2008, 419
Citation in format AMSBIB
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