Skip to main content
SpringerLink
Log in

Some general results for moments in bivariate distributions

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.

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

  • Arnold BC (1995) Conditional survival models. In: Balakrishnan N (eds) Recent advances in life testing and reliability. CRC Press, Boca Raton, pp 589–601

    Google Scholar 

  • Block HW, Feng Z (1988) A multivariate extension of Hoeffding’s lemma. Ann Probab 16(4):1803–1820

    Article  MATH  MathSciNet  Google Scholar 

  • Cuadras CM (2002) On the covariance between functions. J Multivariate Anal 81:19–27

    Article  MATH  MathSciNet  Google Scholar 

  • Gradshteyn IS, Ryzhik IM (1994) Table of integrals, series and products, 5th edn. Academic, San Diego

    Google Scholar 

  • Hutchinson TP, Lai CD (1991) The engineering statistician’s guide to continuous bivariate distributions. Rumsby Scientific Publishing, Australia

    Google Scholar 

  • Kobayashi K (1991) On generalized Gamma functions occurring in diffraction theory. J Phys Soc Jpn 60(5):1501–1512

    Article  Google Scholar 

  • Quesada-Molina JJ (1992) A generalization of an identity of Hoeffding and some applications. J Ital Stat Soc 3:404–411

    Google Scholar 

  • Rudin W (1964) Principles of mathematical analysis. McGraw Hill, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, Orono, ME, 04469-5752, USA

    Ramesh C. Gupta & Henrik Bresinsky

  2. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011, USA

    Mohammad Tajdari

Authors
  1. Ramesh C. Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Tajdari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henrik Bresinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramesh C. Gupta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, R.C., Tajdari, M. & Bresinsky, H. Some general results for moments in bivariate distributions. Metrika 68, 173–187 (2008). https://doi.org/10.1007/s00184-007-0150-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0150-7

Keywords

Search

Navigation