studentt {VGAM}R Documentation

Student t Distribution

Description

Estimation of the degrees of freedom for a Student t distribution.

Usage

studentt(link.df = "loglog", earg=list())

Arguments

link.df Parameter link function for the degrees of freedom nu. See Links for more choices. The default ensures the parameter is greater than unity.
earg List. Extra argument for the link. See earg in Links for general information.

Details

The density function is

f(y) = (gamma((nu+1)/2) / (sqrt(nu*pi) gamma(nu/2))) * (1 + y^2 / nu)^{-(nu+1)/2}

for all real y. Then E(Y)=0 if nu>1 (returned as the fitted values), and Var(Y)= nu/(nu-2) for nu > 2. When nu=1 then the Student t-distribution corresponds to the standard Cauchy distribution. The degrees of freedom is treated as a parameter to be estimated, and as real and not integer.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Note

A standard normal distribution corresponds to a t distribution with infinite degrees of freedom. Consequently, if the data is close to normal, there may be convergence problems.

Author(s)

T. W. Yee

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

Student (1908) The probable error of a mean. Biometrika, 6, 1–25.

See Also

normal1, loglog, TDist.

Examples

n = 500
y = rt(n, df=exp(exp(1)))
fit = vglm(y ~ 1, studentt)
coef(fit, matrix=TRUE)
Coef(fit) 

[Package VGAM version 0.7-4 Index]