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Characterizations of the normal distribution via the independence of the sample mean and the feasible definite statistics with ordered arguments

Author

Listed:
  • Chin-Yuan Hu

    (National Changhua University of Education)

  • Gwo Dong Lin

    (Hwa-Kang Xing-Ye Foundation
    Academia Sinica)

Abstract

It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov’s theorem, we further investigate the analogous characteristic properties in terms of the sample mean and some feasible definite statistics. The latter statistics introduced in this paper for the first time are based on nonnegative, definite and continuous functions of ordered arguments with positive degree of homogeneity. The proposed approach seems to be natural and can be used to derive easily characterization results for many feasible definite statistics, such as known characterizations involving the sample variance, sample range as well as Gini’s mean difference.

Suggested Citation

  • Chin-Yuan Hu & Gwo Dong Lin, 2022. "Characterizations of the normal distribution via the independence of the sample mean and the feasible definite statistics with ordered arguments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 473-488, June.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:3:d:10.1007_s10463-021-00805-3
    DOI: 10.1007/s10463-021-00805-3
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    References listed on IDEAS

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    1. Tea-Yuan Hwang & Chin-Yuan Hu, 1994. "On the joint distribution of studentized order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 165-177, March.
    2. Hwang, Tea-Yuan & Hu, Chin-Yuan, 1994. "The best lower bound of sample correlation coefficient with ordered restriction," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 195-198, February.
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