## Characterization of the S-distribution

S-distributions are univariate statistical distributions with four parameters. They have a simple mathematical structure yet provide excellent approximations for many traditional distributions and also contain a multitude of distributional shapes without a traditional analog. S-distributions furthermore have a number of beneficial features, for instance, in terms of data classification and scaling properties. They provide an appealing compromise between generality in data representation and logistic simplicity and have been applied in a variety of fields from applied biostatistics to survival analysis and risk assessment. Given their advantages in a number of statistical scenarios, it is desirable to explore the features of S-distributions in greater and to extend the concept of S-distributions to generalized forms and to several variates.

*Selected Recent References:*

[1] Voit, E.O.: The S-distribution. A tool for approximation and classification of univariate, unimodal probability distributions. *Biometrical J.* **34(7)**, 855-878, 1992.

[2] Voit, E.O., and P.F. Rust: Invited Tutorial: S-system analysis of continuous univariate probability distributions. J. Stat. Comp. Simul. 42, 187-249, 1992.

[3] Voit, E.O., and S. Yu: The S-distribution. Approximation of discrete distributions. Biometrical J. 36, 205-219, 1994.

[4] Yu, S., and E.O. Voit: A simple, flexible failure model. Biometrical J. 37, 595-609, 1995.

[5] Voit, E.O., W. L. Balthis, and R. A. Holser: Hierarchical Monte Carlo Modeling with S-distributions: Concepts and illustrative analysis of mercury contamination in king mackerel. Environm. Intnl., 21, 627-635, 1995.

[6] Voit, E.O.: Dynamic trends in distributions. Biometrical J. 38 (5), 587-603, 1996.

[7] Voit, E.O., and L.H. Schwacke: Scalability properties of the S-distribution, Biometrical J., 40, 665-684, 1998.

[8] Sorribas, A., J. March, and E.O. Voit: Estimating age-related trends in cross-sectional studies using S-distributions, Stats. in Med. 10(5): 697-713, 2000.

[9] Voit, E.O.: A maximum likelihood estimator for the shape parameters of S-distributions, Biometr. J., 42 (4), 471-479, 2000.

[10] Voit, E.O., and L.H. Schwacke: Random number generation from right-skewed, symmetric, and left-skewed distribution, Risk Analysis 20(1): 59-71, 2000.

[11] Voit, E.O., and A. Sorribas: Computer modeling of dynamically changing distributions of random variables, Mathem. and Computer Modelling 31, 217-225, 2000.

[12] He, Q. and E.O. Voit: Estimation and completion of survival data with piecewise linear models and S-distributions. J. Stat. Comp. Simul. 75(4), 287-305 (2005).

[13] Yu, L., and E.O. Voit: Construction of bivariate S-distributions with copulas. *Comp. Stat. Data Anal.* 51,1822-1839, 2006.

[14] Sorribas, A., J.M. Muiño, and E.O.Voit: GS-distributions: a new family of distributions for continuous unimodal variables. *Comp. Stat. Data Anal.* in press.

[15] Yu, L., and E.O. Voit: Construction of bivariate S-distributions with copulas. Comp. Stat. Data Anal. 51,1822-1839, 2006.

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