studentt {VGAM} | R Documentation |
Estimation of the degrees of freedom for a Student t distribution.
studentt(link.df = "loglog")
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.
|
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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
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.
T. W. Yee
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.
n = 200 y = rt(n, df=exp(2)) fit = vglm(y ~ 1, studentt) coef(fit, matrix=TRUE) Coef(fit)