Skip to main content
SpringerLink
Log in

Test of symmetry of a one-dimensional distribution against positive biasedness

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

Summary

Definitions of different strengths are given to the notion of ‘a positively biased random variable’. This notion is related to that of ‘a stochastically larger component of a two-dimensional random vector’, which was introduced previously by the authors. Properties of common rank tests of symmetry about zero against our specification of alternatives are studied in detail. The positive biasedness is extended to ‘positively more biased’. Test of symmetry of a two-dimensional random vector is also referred to.

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

  1. Hájek, J., Šidák, Z. (1967).Theory of Rank Test, Academic Press, New York.

    Google Scholar 

  2. Lehmann, E. L. (1959).Testing Statistical Hypotheses, John Wiley, New York.

    Google Scholar 

  3. Savage, I. R. (1959). Contributions to the theory of rank order statistics—the one sample case,Ann. Math. Statist.,30, 1018–1023.

    MATH  MathSciNet  Google Scholar 

  4. Yanagimoto, T. and Okamoto, M. (1969). Partial orderings of permutations and monotonicity of a rank correlation statistic,Ann. Inst. Statist. Math.,21, 489–506.

    MATH  MathSciNet  Google Scholar 

  5. Yanagimoto, T. and Sibuya, M. (1972). Stochastically larger component of a random vector,Ann. Inst. Statist. Math.,24, 259–269.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics, IBM Japan, Scientific Center, Japan

    Takemi Yanagimoto & Masaaki Sibuya

Authors
  1. Takemi Yanagimoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaaki Sibuya
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Yanagimoto, T., Sibuya, M. Test of symmetry of a one-dimensional distribution against positive biasedness. Ann Inst Stat Math 24, 423–434 (1972). https://doi.org/10.1007/BF02479771

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479771

Keywords

Search

Navigation