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(), idf=NULL, nsimEIM=100)

### 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.
`idf` | Optional initial value. If given, its value must be greater than 1. The default is to compute an initial value internally.
`nsimEIM` | See `CommonVGAMffArguments`.

### 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.

Simulation is used to estimate the EIM. Consequently the results will be reproducible only if a function such as `set.seed` is used. Increasing the value of `nsimEIM` will give more accurate results. In general convergence will be slow, especially when there are covariates.

### Value

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

### Note

Practical experience has shown reasonably good initial values are required. If convergence failure occurs try using `idf`. Local solutions are also possible.

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(0.5)))
    fit = vglm(y ~ 1, studentt, trace=TRUE)
    coef(fit, matrix=TRUE)
    Coef(fit)

[Package VGAM version 0.7-9 Index]