Skip to main content
Log in

The log F: A Distribution for All Seasons

  • Published:
Computational Statistics Aims and scope Submit manuscript

Summary

Families of parametric models are widely used to summarize data, to obtain predictions, assess goodness of fit, to estimate functions of the data not easily derived directly, and to render manageable random effects. The trustworthiness of the results obtained depends on the generality of the parametric family employed. A very flexible set of statistical models based on the logarithm of an F variate was introduced over 20 years ago. It’s versatility appears to be little appreciated by the statistical community. We try to convince readers that this family belongs in the tool box of all applied statisticians and that it should be one of the first tools used in data exploration. We present examples that cover a variety of statistical functions and application areas, and we offer freely available computer code.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Similar content being viewed by others

References

  • Brown, B. W., Brauner, C. and Levy, L. B. (1997), Assessing Changes in the Impact of Cancer on Population Survival Without Considering Cause of Death Journal of the National Cancer Institute 89, 58–65.

    Article  Google Scholar 

  • Brown, B. W., Levy, L. B. (1994) Certification of Algorithm 708: Significant Digit Computation of the Incomplete Beta. ACM Transactions on Mathematical Software, 20, 393–397.

    Article  Google Scholar 

  • Brown, B. W., Spears, F. M., Levy, L. B., Lovato, J., and Russell, K. (1996), Algorithm 762: LLDRLF, Log-Likelihood and Some Derivatives for Log-F Models. ACM Transactions on Mathematical Software, 22, 372–382.

    Article  Google Scholar 

  • Di Donato, A. R., and Morris, A. H. (1992), Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Transactions on Mathematical Software, 18, 360–373.

    Article  Google Scholar 

  • Gay, D.M. (1983), Algorithm 611. Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach. ACM Transactions on Mathematical Software 9, 503–524.

    Article  MathSciNet  Google Scholar 

  • Hogg, S. A. and Ciampi, A. (1985), GFREG: A Computer Program for Maximum Likelihood Regression using the Generalized F Distribution. Computer Methods and Programs in Biomedicine 20, 201–215.

    Article  Google Scholar 

  • Kalbfleish, J. D. and Prentice, R. L. (1980),The Statistical Analysis of Failure Time Data. John Wiley and Sons, New York.

    Google Scholar 

  • Mack, W., Langholz, B. and Thomas, D. C. (1990), Survival Models for Familial Aggregation of Cancer. Environmental Health Perspectives 87, 27–35.

    Article  Google Scholar 

  • Peng, Y., Dear, K.B.G., and Denham, J.W. (1998), A Generalized F Mixture Model for Cure Rate Estimation. Statistics in Medicine 17, 813–830.

    Article  Google Scholar 

  • Prentice, R. L. (1975), Discrimination among Some Parametric Models. Biometrika, 62, 607–614.

    Article  MathSciNet  Google Scholar 

  • Prentice, R. L. (1976),A Generalization of the Probit and Logit Methods for Dose Response Curves. Biometrics, 32, 761–768.

    Article  Google Scholar 

  • SEER (1997), Surveillance, Epidemiology, and End Results public use CDROM (1973–1995). National Cancer Institute, Division of Cancer Prevention and Control, Surveillance Program, Cancer Statistics Branch.

  • Taylor, B. (1998), Stock Market Indices, 1800–1995. URL http://www.globalfindata.com. Used with permission.

  • U.S.A. Today (1998), AL team-by-team statistics. URL http://www.usatoday.com. Used with permission.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Brown, B.W., Spears, F.M. & Levy, L.B. The log F: A Distribution for All Seasons. Computational Statistics 17, 47–58 (2002). https://doi.org/10.1007/s001800200098

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001800200098

Keywords

Navigation