Skip to main content
SpringerLink
Log in

Tolerance regions for a multivariate normal population

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

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

References

  1. S. Geisser, “The distribution of the ratios of certain quadratic forms in time series,” Ann. Math. Statist., 28 (1957), 724–730.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Grad and H. Solomon, “Distribution of quadratic forms and some applications,” Ann. Math. Statist., 26 (1955), 464–477.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Gurland, “Distribution of definite and of indefinite quadratic forms,” Ann. Math. Statist., 26 (1955), 122–127.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Gurland, “Quadratic forms in normally distributed random variables,” Sankhya, 17 (1956), 37–50.

    MathSciNet  MATH  Google Scholar 

  5. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge, 1934.

  6. A. G. Laurent, “Definite quadratic forms and discontinuous factor,” Ann. Math. Statist., 27 (1956), 865–866.

    Google Scholar 

  7. M. Okamoto, “An inequality for the weighted sum of x2 variates,” Bull. Math. Statist., 9 (1960), 69–70.

    MathSciNet  MATH  Google Scholar 

  8. J. Pachares, “Note on the distribution of a definite quadratic form,” Ann. Math. Statist., 26 (1955), 128–131.

    Article  MathSciNet  MATH  Google Scholar 

  9. K. Pearson (editor), Tables of the Incomplete Gamma-Function, Biometrika office, London, 1951.

    Google Scholar 

  10. H. Robbins, “The distribution of a definite quadratic form,” Ann. Math. Statist., 19 (1948), 266–270.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. N. Roy and R. C. Bose, “Simultaneous confidence interval estimation,” Ann. Math. Statist., 24 (1953), 513–536.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. N. Roy, “Some further results in simultaneous confidence interval estimation,” Ann. Math. Statist., 25 (1954), 752–761.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. N. Roy and R. Gnanadesikan, “Further contributions to multivariate confidence bounds,” Biometrika, 44 (1957), 289–292.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. N. Roy, Some Aspects of Multivariate Analysis, John Wiley and Sons, New York, 1957.

    Google Scholar 

  15. S. N. Roy and R. E. Bargmann, “Tests of multiple independence and the associated confidence bounds,” Ann. Math. Statist., 29 (1958), 491–503.

    Article  MathSciNet  MATH  Google Scholar 

  16. S. N. Roy and R. E. Potthoff, “Confidence bounds on vector analogues of the ‘ratio of means” and the ‘ratio of variances’ for two correlated normal variates and some associated tests,” Ann. Math. Statist., 29 (1958), 829–841.

    Article  MathSciNet  MATH  Google Scholar 

  17. B. K. Shah and C. G. Khatri, “Distribution of a definite quadratic form for noncentral normal variates,” Ann. Math. Statist., 32 (1961), 883–887.

    Article  MathSciNet  MATH  Google Scholar 

  18. H. Solomon, “On the distribution of quadratic forms in normal variables,” Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles, University of California, I (1961), 645–653.

    Google Scholar 

  19. A. Wald and J. Wolfowitz, “Tolerance limits for a normal distribution,” Ann. Math. Statist., 17 (1946), 208–215.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Statistical Mathematics and Stanford University, USA

    Mlnoru Slotani

Authors
  1. Mlnoru Slotani
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by National Science Foundation Grant Number 214 at Stanford University.

About this article

Cite this article

Slotani, M. Tolerance regions for a multivariate normal population. Ann Inst Stat Math 16, 135–153 (1964). https://doi.org/10.1007/BF02868568

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02868568

Keywords

Search

Navigation