# studentt: The Student-t Distribution (Location-Scale) In stevemisc: Steve's Miscellaneous Functions

 studentt R Documentation

## The Student-t Distribution (Location-Scale)

### Description

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.

### 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).

### Value

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

`TDist`