## The Student t Distribution

## Usage

    dt(x, df)
    pt(q, df, ncp=0)
    qt(p, df)
    rt(n, df)

## Arguments

`x,q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations to generate.
`df,ncp` | degrees of freedom and non-centrality parameter.

## Description

These functions provide information about the t distribution with `df` degrees of freedom (and optional noncentrality parameter `ncp`). `dt` gives the density, `pt` gives the distribution function, `qt` gives the quantile function and `rt` generates random deviates.

The t distribution with `df` = n degrees of freedom has density

f(x) = Gamma((n+1)/2) / (sqrt(n pi) Gamma(n/2)) (1 + x^2/n)^-((n+1)/2)

for all real x.

## See Also

`df` for the F distribution.

## Examples

    1 - pt(1:5, df = 1)
    qt(.975, df = c(1:10,20,50,100,1000))

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