Skip to main content
SpringerLink
Log in

Error Bounds for Trapezoid Type Quadrature Rules with Applications for the Mean and Variance

  • Chapter
  • First Online:
Applications of Mathematics and Informatics in Science and Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 91))

  • 1525 Accesses

Abstract

In this paper, we establish some inequalities of trapezoid type to give tight bounds for the expectation and variance of a probability density function. The approach is also demonstrated for higher order moments.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barnett, N.S., Cerone P., and Dragomir, S.S.: Inequalities for distributions on a finite interval. Advances in Mathematical Inequalities Series. Nova Science Publishers Inc., New York (2008)

    MATH  Google Scholar 

  2. Brnetić, I. and Pečarić, J.: On an Ostrowski type inequality for a random variable. Math. Inequal. Appl. 3, No. 1, 143–145 (2000)

    MATH  MathSciNet  Google Scholar 

  3. Cacoullos, T. Variance inequalities, characterizations, and a simple proof of the central limit theorem. Data analysis and statistical inference, 27–32 (1992)

    Google Scholar 

  4. Cacoullos, T. and Papadatos, N. and Papathanasiou, V.: Variance inequalities for covariance kernels and applications to central limit theorems. Teor. Veroyatnost. i Primenen. 42, No. 1, 195–201 (1997)

    Google Scholar 

  5. Cerone P., and Dragomir S.S.: Trapezoid type rules from an inequalities point of view. Handbook of Analytic Computational Methods in Applied Mathematics. Anastassiou G. (Ed.), pp. 65–134. CRC Press, N.Y. (2000)

    Google Scholar 

  6. Chang, W-Y. and Richards, D.St.P.: Variance inequalities for functions of multivariate random variables. Contemp. Math. 234, 43–67 (1999)

    Google Scholar 

  7. Chernoff, H.: A note on an inequality involving the normal distribution. Ann. Probab. 9, No. 3, 533–535 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dharmadhikari, S. W. and Joag-Dev, K.: Upper bounds for the variances of certain random variables. Comm. Statist. Theory Methods 18, No. 9, 3235–3247 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Houdré, C. and Kagan, A.: Variance inequalities for functions of Gaussian variables. J. Theoret. Probab. 8, No. 1, 23–30 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Prakasa Rao, B. L. S. and Sreehari, M.: Chernoff-type inequality and variance bounds. J. Statist. Plann. Inference 63, No. 2, 325–335 (1997)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, La Trobe University, Bundoora, 3086, Australia

    Pietro Cerone

  2. School of Engineering and Science, Victoria University, Melbourne, 8001, Australia

    Sever S. Dragomir

  3. School of Computational and Applied Mathematics, University of the Witwatersrand, Witwatersrand, South Africa

    Sever S. Dragomir

  4. Department of Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    Eder Kikianty

Authors
  1. Pietro Cerone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sever S. Dragomir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eder Kikianty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eder Kikianty .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Engineering Sciences, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Cerone, P., Dragomir, S.S., Kikianty, E. (2014). Error Bounds for Trapezoid Type Quadrature Rules with Applications for the Mean and Variance. In: Daras, N. (eds) Applications of Mathematics and Informatics in Science and Engineering. Springer Optimization and Its Applications, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-04720-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation