The T_PDF function computes the cumulative distribution function for a Student's *t* distribution with *Df* degrees of freedom. This is the probability *P* that, in a Student’s t distribution, a random variable *X* is less than or equal to a user-specified cutoff value *V*.

**Note: **T_PDF computes the one-tailed probability. The two-tailed probability, which is the probability that the absolute value of *X* is less than or equal to *V*, can be computed as 1 - 2 x (1 - T_PDF(*V*, *Df*)).

This routine is written in the IDL language. Its source code can be found in the file t_pdf.pro in the lib subdirectory of the IDL distribution.

## Examples

Use the following command to compute the probability that a random variable X, from the Student’s t distribution with 15 degrees of freedom, is less than or equal to 0.691:

PRINT, T_PDF(0.691, 15)

IDL prints:

0.749940

## Syntax

*Result* = T_PDF(*V*,* Df*)

## Return Value

If both arguments are scalar, the function returns a scalar. If both arguments are arrays, the function matches up the corresponding elements of *V* and *Df*, returning an array with the same dimensions as the smallest array. If one argument is a scalar and the other argument is an array, the function uses the scalar value with each element of the array, and returns an array with the same dimensions as the input array.

If any of the arguments are double-precision, the result is double-precision, otherwise the result is single-precision.

## Arguments

### V

A scalar or array that specifies the cutoff value(s).

### Df

A scalar or array that specifies the number of degrees of freedom of the Student’s t distribution.

## Keywords

None.

## Version History

4.0 |
Introduced |

## See Also

BINOMIAL, CHISQR_PDF, F_PDF, GAUSS_PDF, T_CVF