Skip to main content
SpringerLink
Log in

Interval Estimation of Probability P(X < Y) in Case of One-Parameter Exponential Families Using Unbiased Estimates*

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

In this paper on the basis of unbiased estimates the problem of constructing asymptotic confidence interval for P(X < Y) is solved for the case where random variables X and Y have distributions, belonging to one-parameter exponential families.

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. V.V. Ivshin and Ya.P. Lumelsky, Statistical Problems of Estimation in the “Stress–Strength” Model [in Russian], Perm University Press, Perm (1995).

    Google Scholar 

  2. Ya.P. Lumelskii and P.D. Feigin, “Unbiased estimates of variance in parametrical case,” J. Math. Sci., 189, No. 6, 903–910 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  3. M.A. Oleynik and V.V. Chichagov, “Asymptotic normality of unbiased estimates in case of absolutely continuous multivariate exponential family,” J. Math. Sci., 189, No. 6, 976–982 (2013).

    Article  MathSciNet  Google Scholar 

  4. V. V. Petrov, Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  5. V.V. Chichagov, “Concerning asymptotic normality of a class of unbiased estimators in the case of absolutely continuous distributions,” J. Math. Sci., 119, No. 3, 336–341 (2004).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Perm State University, Perm, Russia

    V. V. Chichagov & M. A. Oleynik

Authors
  1. V. V. Chichagov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Oleynik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Chichagov.

Additional information

*This research is supported by RFBR, project №05–01–00229 and by Russian Ministry of Education and Science, project №2096.

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 18, pp. 73–87, 2005

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chichagov, V.V., Oleynik, M.A. Interval Estimation of Probability P(X < Y) in Case of One-Parameter Exponential Families Using Unbiased Estimates*. J Math Sci 205, 45–54 (2015). https://doi.org/10.1007/s10958-015-2228-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2228-5

Keywords

Search

Navigation