Abstract
The S-distribution is defined in the form of a four-parameter nonlinear differential equation, with the cumulative distribution function of the survival time as the dependent variable and the survival time as the independent variable. The first parameter characterizes the location, the second the scale, and the other two the shape of the model. The S-distribution covers the logistic distribution and the exponential distribution as special cases and approximates other common survival models with rather high precision. The S-distribution is used to classify common survival distributions within a two-dimensional space in which characteristics related to the shape of the density function and the hazard function can be studied. Nonlinear regression methods are used in the classification procedure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cox, D.R., and Oakes, D. (1984), Analysis of Survival Data, New York, NY: Chapman and Hall. Gehan, E.A. (1965), “A Generalized Wilcoxon Text for Comparing Arbitrarily Single-Censored Samples,” Biometrika, 52, 203–523.
Gross, A.J., and Clark, V.A. (1975), Survival Distributions: Reliability Applications in the Biomedical Sciences, New York, NY: Wiley.
Halley, E. (1693), “An Estimate of the Degrees of the Mortality of Mankind, Drawn From Curious Tables of the Births and Funerals of the City of Breslau,” Philosophical Transactions of the Royal Society of London, 17, 596–610.
Johnson, N.L., and Kotz, S. (1970), Continuous Univariate Distributions, Boston: Houghton Miffl in Co.
Kalbfleisch, J.D. and Prentice, R.L. (1980), Survival Models and Data Analysis, New York, NY: John Wiley & Sons, Inc.
Kaplan, E.L. and Meier P. (1958), “Nonparametric Estimation From Incomplete Observations.,” Journal of the American Statistical Association, 53, 457–481.
Prentice, R.L. (1975), “Discrimination Among Some Parametric Models,” Biometrika, 62, 607614.
Ralston, M.L., Jennrich, R.I., Sampson, P.F., and Uno, F.K. (1988), “Fitting Pharmacokinetic Models With Program AR: New Instructions for PCs and Mainframes,” BMDP Technical Report, #85. Los Angeles: BMDP Statistical Software, Inc.
Voit, E.O. (1991), “Canonical Nonlinear Modeling, S-System Approach to Understanding Complexity,” New York, NY: Van Nostrand Reinhold.
Voit, E.O. (1992), “The S-distribution: a Tool for Approximation and Classification of Univariate
Unimodal Probability Distributions,“ Biometrical Journal,34, (1992) 7, 855–878.
Voit, E.O., and Yu, S. (1994), “The S-distribution: Approximation of Discrete Distributions.,” Biometrical Journal, 36, (1994) 2, 205–219.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Yu, S.S., Vorr, E.O. (1996). A Graphical Classification of Survival Distributions. In: Jewell, N.P., Kimber, A.C., Lee, ML.T., Whitmore, G.A. (eds) Lifetime Data: Models in Reliability and Survival Analysis. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5654-8_50
Download citation
DOI: https://doi.org/10.1007/978-1-4757-5654-8_50
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4753-6
Online ISBN: 978-1-4757-5654-8
eBook Packages: Springer Book Archive