Documentation

# `stats`::`tPDF`

Probability density function of Student's t-distribution

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## Syntax

```stats::tPDF(`a`)
```

## Description

`stats::tPDF(a)` returns a procedure representing the probability density function of Student's t-distribution with shape parameter ('degrees of freedom') `a > 0`.

The procedure `f := stats::tPDF(a)` can be called in the form `f(x)` with an arithmetical expression `x`. The return value of `f(x)` is either a floating-point number or a symbolic expression:

If `x` is a floating-point number and `a` can be converted to a floating-point number, then `f(x)` returns a floating-point number.

`f(infinity)` and `f(-infinity)` produce the result `0.0`.

In all other cases, the expression is returned.

If floating-point results are desired, call `f(x)` with a floating-point value `x`.

Numerical values for `a` are only accepted if they are real and positive.

## Examples

### Example 1

We evaluate the probability density function with `a` = at various points:

```f := stats::tPDF(3/4): f(-infinity), f(-PI), f(1/2), f(0.5), f(3), f(infinity)```
` `
`delete f:`

### Example 2

We use symbolic arguments:

`f := stats::tPDF(a): f(x), f(0.3)`
` `

When numerical values are assigned to `a`, the function `f` starts to produce floating-point values for floating-point arguments:

`a := PI: f(0.3)`
` `
`delete f, a:`

## Parameters

 `a` The shape parameter: an arithmetical expression representing a positive real value