Skip to main content
SpringerLink
Log in

Exact computations for the coherence estimate

  • Technical Note
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

The recent paper by Miranda de Sa et al. [10] developed methods for computing the sampling distribution of the coherence estimate between two signals. However, the methods were based on some approximations because it was claimed that exact calculations required extensive computations. In this technical note, we provide analytical expressions and 1-line programs for the exact computation of various measures of the sampling distribution. Besides being exact, our programs have several advantages over the methods suggested in [10].

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. Chattamvelli R (1995) On the doubly noncentral F distribution. Comput Stat Data Anal 20:481–489

    Article  MATH  Google Scholar 

  2. Chattamvelli R (1995) A note on the noncentral beta distribution function. Am Stat 49:231–234

    Article  Google Scholar 

  3. Chen ZY, Zhou YC (2000) Computing the noncentral beta distribution with S-system. Comput Stat Data Anal 33:343–360

    Article  MATH  Google Scholar 

  4. Ding CG (1992) Algorithm AS 275: computing the noncentral χ2 distribution function. Appl Stat 41:478–482

    Article  Google Scholar 

  5. Ding CG (1994) On the computation of the noncentral beta distribution. Comput Stat Data Anal 18:449–455

    Article  MATH  Google Scholar 

  6. Hodges JL (1955) On the noncentral beta-distribution. Ann Math Stat 26:648–653

    Google Scholar 

  7. Ihaka R, Gentleman R (1996) R: a language for data analysis and graphics. J Comput Graph Stat 5:299–314

    Article  Google Scholar 

  8. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  9. Marchand E (1997) On moments of beta mixtures, the noncentral beta distribution, and the coefficient of determination. J Stat Comput Simul 59:161–178

    Article  MATH  Google Scholar 

  10. Miranda de Sa AMFL, Infantosi AFC, Simpson DM (2002) Coherence between one random and one periodic signal for measuring the strength of responses in the electro-encephaloogram during sensory stimulation. Med Biol Eng Comput 40:99–104

    Article  Google Scholar 

  11. Nicholson WL (1954) A computing formula for the power of the analysis of variance test. Ann Math Stat 25:607–610

    Google Scholar 

  12. Patnaik PB (1949) The noncentral χ2- and F-distribution and their applications. Biometrika 36:202–232

    MATH  Google Scholar 

  13. Seber GAF (1963) The non-central Chi-squared and beta distributions. Biometrika 50:542–544

    MATH  Google Scholar 

  14. Tang PC (1938) The power function of the analysis of variance test with tables and illustrations of their use. Stat Res Mem 2:126–149

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

  2. George Washington University, Washington, DC, 20052, USA

    Samuel Kotz

Authors
  1. Saralees Nadarajah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samuel Kotz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saralees Nadarajah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadarajah, S., Kotz, S. Exact computations for the coherence estimate. Med Bio Eng Comput 45, 701–705 (2007). https://doi.org/10.1007/s11517-007-0203-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-007-0203-0

Keywords

Search

Navigation