Skip to main content
SpringerLink
Log in

On a Characterization of the Gamma Distribution: The Independence of the Sample Mean and the Sample Coefficient of Variation

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Let n≥ 3 and let X 1,...,X n be positive i.i.d. random variables whose common distribution function f has a continuous p.d.f. Using earlier work of the present authors and a method due to Anosov for solving certain integro-functional equations, it is shown that the independence of the sample mean and the sample coefficient of variation is equivalent to that f is a gamma function. While the proof is of methodological interest, this conclusion can also be arrived at without any assumptions by appealing to the Laplace-Stieltjes transform, as in the Concluding Romark (Section 3).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Anosov, D. V. (1964). On an integral equation arising in statistics, Vestnik Leningrad University, 7, 151–154.

    Google Scholar 

  • Hwang, T. Y. and Hu, C. Y. (1994). On the joint distribution of studentized order statistics, Ann. Inst. Statist. Math., 46, 165–177.

    Google Scholar 

  • Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions-1, Houghton Miffin Co., Boston.

    Google Scholar 

  • Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973). Characterization Problems in Mathematical Statistics (translated by B. Ramachandran), Wiley, New York.

    Google Scholar 

  • Lukacs, E. and Laha, R. G. (1964). Applications of Characteristic Functions, Hafner, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Statistics, National Tsing Hua University, Hsinchu, 30043, Taiwan, R.O.C

    Tea-Yuan Hwang

  2. Department of Business Education, National Changhua University of Education, Changhua, 50058, Taiwan, R.O.C

    Chin-Yuan Hu

Authors
  1. Tea-Yuan Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Yuan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Hwang, TY., Hu, CY. On a Characterization of the Gamma Distribution: The Independence of the Sample Mean and the Sample Coefficient of Variation. Annals of the Institute of Statistical Mathematics 51, 749–753 (1999). https://doi.org/10.1023/A:1004091415740

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004091415740

Search

Navigation