Abstract:
There are properties which characterize the gamma distribution via
independence of two appropriately chosen statistics. Well known is the
classical result when one of the statistics is the sample mean and the other
is the sample coefficient of variation. In this paper, we elaborate on
a version of Anosov's theorem, which allows us to establish a general result and a series of seven corollaries, providing new
characterization results for gamma distributions. We keep the sample mean as
one of involved statistics, while the other can be taken from
a quite large class of homogeneous feasible definite statistics. We discuss an interesting parallel between the new characterization results
for gamma distributions and recent characterization results for the normal
distribution.
Keywords:
characterization of the gamma distribution, sample mean, sample coefficient of variation, order statistics, feasible statistics, sample size, Gini coefficient, Anosov's theorem.
Citation:
Lin G. D., J. M. Stoyanov, “New characterizations of the Gamma distribution via independence of two statistics by using Anosov’s theorem”, Teor. Veroyatnost. i Primenen., 69:4 (2024), 745–759; Theory Probab. Appl., 69:4 (2025), 592–604
\Bibitem{LinSto24}
\by Lin~G.~D., J.~M.~Stoyanov
\paper New characterizations of the Gamma distribution via independence of two statistics by using Anosov’s theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 2024
\vol 69
\issue 4
\pages 745--759
\mathnet{http://mi.mathnet.ru/tvp5593}
\crossref{https://doi.org/10.4213/tvp5593}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 69
\issue 4
\pages 592--604
\crossref{https://doi.org/10.1137/S0040585X97T99215X}
Citation in format AMSBIB
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