The Student-t Distribution (Location-Scale)

These are density, distribution function, quantile function and random generation for the Student-t distribution with location mu, scale sigma, and degrees of freedom df. Base R gives you the so-called "standard" Student-t distribution, with just the varying degrees of freedom. This generalizes that standard Student-t to the three-parameter version.

Usage

dst(x, df, mu, sigma)

pst(q, df, mu, sigma)

qst(p, df, mu, sigma)

rst(n, df, mu, sigma)

Arguments

x, q

a vector of quantiles

df

a vector of degrees of freedom

mu

a vector for the location value

sigma

a vector of scale values

p

Vector of probabilities.

n

Number of samples to draw from the distribution.

Value

dst() returns the density. pst() returns the distribution function. qst() returns the quantile function. rst() returns random numbers.

Details

This is a simple hack taken from Wikipedia. It's an itch I've been wanting to scratch for a while. I can probably generalize this outward to allow the tail and log stuff, but I wrote this mostly for the random number generation. Right now, I haven't written this to account for the fact that sigma should be non-negative, but that's on the user to know that (for now).

See also

TDist