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NEW CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION VIA INDEPENDENCE OF TWO STATISTICS BY USING ANOSOV'S THEOREM.

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Title: NEW CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION VIA INDEPENDENCE OF TWO STATISTICS BY USING ANOSOV'S THEOREM.
Authors: LIN, G. D.1 gdlin@stat.sinica.edu.tw, STOYANOV, J. M.2 stoyanovj@gmail.com
Source: Theory of Probability & Its Applications. 2024, Vol. 69 Issue 4, p592-604. 13p.
Subjects: Gamma distributions, Statistics, Distribution (Probability theory), Mathematical statistics, Standard deviations
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. [ABSTRACT FROM AUTHOR]
Copyright of Theory of Probability & Its Applications is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: NEW CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION VIA INDEPENDENCE OF TWO STATISTICS BY USING ANOSOV'S THEOREM.
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  Data: <searchLink fieldCode="JN" term="%22Theory+of+Probability+%26+Its+Applications%22">Theory of Probability & Its Applications</searchLink>. 2024, Vol. 69 Issue 4, p592-604. 13p.
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theory of Probability & Its Applications is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/S0040585X97T99215X
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      – Code: eng
        Text: English
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        PageCount: 13
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      – SubjectFull: Gamma distributions
        Type: general
      – SubjectFull: Statistics
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Mathematical statistics
        Type: general
      – SubjectFull: Standard deviations
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      – TitleFull: NEW CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION VIA INDEPENDENCE OF TWO STATISTICS BY USING ANOSOV'S THEOREM.
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              Text: 2024
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