Skip to main content
SpringerLink
Log in

Generalized F Tests in Models with Random Perturbations: The Truncated Normal Case

  • Conference paper
  • First Online:
Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

  • 3382 Accesses

Abstract

This paper shows how to obtain explicit expressions for non-central generalized F distributions with random non-centrality parameters. We consider the case when these parameters are random variables with truncated Normal distribution, for the usual F distribution and for the generalized F distribution.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Davies, R.B.: Algorithm AS 155: The distribution of a linear combinations of χ 2 random variables. Appl. Stat. 29, 232–333 (1980)

    Google Scholar 

  2. Fonseca, M., Mexia, J.T., Zmyślony, R.: Exact distribution for the generalized F tests. Discuss. Math. Probab. Stat. 22, 37–51 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Gaylor, D.W., Hopper, F.N.: Estimating the degrees of freedom for linear combinations of mean squares by Satterthwaite’s formula. Technometrics 11, 691–706 (1969)

    Article  Google Scholar 

  4. Imhof, J.P.: Computing the distribution of quadratic forms in normal variables. Biometrika 48, 419–426 (1961)

    MathSciNet  MATH  Google Scholar 

  5. Michalski, A., Zmyślony, R.: Testing hypothesis for variance components in mixed linear models. Statistics 27, 297–310 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Michalski, A., Zmyślony, R.: Testing hypothesis for linear functions of parameters in mixed linear models. Tatra Mt. Math. Publs. 17, 103–110 (1999)

    MATH  Google Scholar 

  7. Nunes, C., Mexia, J.T.: Non-central generalized F distributions. Discuss. Math. Probab. Stat. 26, 47–61 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Nunes, C., Ferreira, S., Ferreira, D.: Generalized F tests in models with random perturbations: The Gamma case. Discuss. Math. Probab. Stat. 29(2), 185–198 (2009)

    MathSciNet  MATH  Google Scholar 

  9. Nunes, C., Ferreira, D., Ferreira, S., Mexia, J.T.: Generalized F distributions with random non-centrality parameters: The convolution of Gamma and Beta variables. Far East J. Math. Sci. 62(1), 1–14 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Robbins, H.: Mixture of distribution. Ann. Math. Statist. 19, 360–369 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  11. Robbins, H., Pitman, E.J.G.: Application of the method of mixtures to quadratic forms in normal variates. Ann. Math. Statist. 20, 552–560 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  12. Satterthwaite, F.E.: An approximate distribution of estimates of variance components. Biometrics Bull. 2, 110–114 (1946)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the anonymous referees for their useful comments and remarks. This work was partially supported by the center of Mathematics, University of Beira Interior, under the project PEst-OE/MAT/UI0212/2011.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Beira Interior, Covilhã, Portugal

    Célia Nunes, Dário Ferreira & Sandra Ferreira

  2. Department of Mathematics, New University of Lisbon, Caparica, Portugal

    João T. Mexia

Authors
  1. Célia Nunes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dário Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sandra Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. João T. Mexia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Célia Nunes .

Editor information

Editors and Affiliations

  1. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    João Lita da Silva

  2. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    Frederico Caeiro

  3. , Universidade Nova de Lisboa, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica, Caparica, 2829-516, Portugal

    Isabel Natário

  4. , Universidade Nova de Lisboa,, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica 59, Caparica, 2829-516, Portugal

    Carlos A. Braumann

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nunes, C., Ferreira, D., Ferreira, S., Mexia, J.T. (2013). Generalized F Tests in Models with Random Perturbations: The Truncated Normal Case. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_32

Download citation

Publish with us

Policies and ethics

Search

Navigation