Skip to main content
SpringerLink
Log in

Correlation in a singly truncated bivariate normal distribution

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The correlation in a singly truncated binormal distribution is obtained in terms of Mills' ratio using the Mehler identity. A table of the correlation in the underlying distribution as a function of the correlation in the truncated distribution is presented, together with a diagram summarizing this relationship.

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. Birnbaum, Z. W. Effect of linear truncation on a multinormal population.Ann. math. Statist., 1950,21, 272–279.

    Google Scholar 

  2. Birnbaum, Z. W. and Meyer, P. L. On the effect of truncation in some or all coordinates of a multinormal population.J. Ind. Soc. agric. Statist., 1953,5, 18–28.

    Google Scholar 

  3. Birnbaum, Z. W., Paulson, E., and Andrews, F. C. On the effect of selection performed on some coordinates of a multidimensional population.Psychometrika, 1950,15, 191–204.

    Google Scholar 

  4. Cohen, A. C. Restriction and selection in samples from bivariate normal distributions.J. Amer. statist. Ass., 1955,50, 884–893.

    Google Scholar 

  5. Cohen, A. C. On the solution of estimating equations for truncated and censored samples from normal populations.Biometrika, 1957,44, 225–236.

    Google Scholar 

  6. Cohen, A. C. Restriction and selection in multinormal distributions.Ann. math. Statist., 1957,28, 731–741.

    Google Scholar 

  7. Gordon, R. D. Value of Mills' ratio of area to bounding ordinate of the normal probability integral for large values of the argument.Ann. math. Statist., 1941,12, 364–366.

    Google Scholar 

  8. Kendall, M. G. Proof of relations connected with the tetrachoric series and its generalisation.Biometrika, 1941,32, 196–198.

    Google Scholar 

  9. Mehler, F. G. Uber die Entwicklung einer Funktion von beliebig vielen Variablen nach Laplaceschen Funktionen hoherer Ordnung.J. Fur. Mathematik, 1866,66, 161–176.

    Google Scholar 

  10. Mills, J. P. Table of ratio: area to bounding ordinate, for any portion of the normal curve.Biometrika, 1926,18, 395–400.

    Google Scholar 

  11. Raj, D. On estimating the parameters of bivariate normal populations from doubly and singly linearly truncated samples.Sankhya, 1953,12, 277–290.

    Google Scholar 

  12. Szego, G.Orthogonal polynomials. A.M.S. Colloq. Publ. XXIII, 1939.

  13. Votaw, D. F., Rafferty, J. A., and Deemer, W. L. Estimation of parameters in a truncated trivariate normal distribution.Psychometrika, 1950,15, 339–347.

    Google Scholar 

  14. Weiler, H. Means and standard deviations of a truncated bivariate normal distribution.Aust. J. Statist., 1959,1, 73–81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Sydney, Sydney, N. S. W.

    M. A. Aitkin

Authors
  1. M. A. Aitkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I wish to express my appreciation to Professor H. O. Lancaster of the Department of Mathematical Statistics, Sydney University, for the suggestion of this problem.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aitkin, M.A. Correlation in a singly truncated bivariate normal distribution. Psychometrika 29, 263–270 (1964). https://doi.org/10.1007/BF02289723

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02289723

Keywords

Search

Navigation