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.
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.
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.
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.
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.
Gay, D.M. (1983), Algorithm 611. Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach. ACM Transactions on Mathematical Software 9, 503–524.
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.
Kalbfleish, J. D. and Prentice, R. L. (1980),The Statistical Analysis of Failure Time Data. John Wiley and Sons, New York.
Mack, W., Langholz, B. and Thomas, D. C. (1990), Survival Models for Familial Aggregation of Cancer. Environmental Health Perspectives 87, 27–35.
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.
Prentice, R. L. (1975), Discrimination among Some Parametric Models. Biometrika, 62, 607–614.
Prentice, R. L. (1976),A Generalization of the Probit and Logit Methods for Dose Response Curves. Biometrics, 32, 761–768.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s001800200098