Routines (alphabetical) > Routines: G > GAUSS_PDF

# GAUSS_PDF

The GAUSS_PDF function computes the cumulative distribution function for a standard Gaussian (normal) distribution. This is the probability P that, in a Gaussian distribution with a mean of 0.0 and a variance of 1.0, a random variable X is less than or equal to a user-specified cutoff value V.

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

## Examples

### Example 1

Compute the probability that a random variable X, from the standard Gaussian (normal) distribution, is less than or equal to 2.44:

PRINT, GAUSS_PDF(2.44)

IDL Prints:

0.992656

### Example 2

Compute the probability that a random variable X, from the standard Gaussian (normal) distribution, is less than or equal to 10.0 and greater than or equal to 2.0:

PRINT, GAUSS_PDF(10.0) - GAUSS_PDF(2.0)

IDL Prints:

0.0227501

### Example 3

Compute the probability that a random variable X, from the Gaussian (normal) distribution with a mean of 0.8 and a variance of 4.0, is less than or equal to 2.44:

PRINT, GAUSS_PDF( (2.44 - 0.80)/SQRT(4.0) )

IDL Prints:

0.793892

## Syntax

Result = GAUSS_PDF(V)

## Return Value

This function returns a scalar or array with the same dimensions as V. If V is 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).

## Keywords

None.

## Version History

4.0 | Introduced

## See Also

BINOMIAL, CHISQR_PDF, F_PDF, GAUSS_CVF, T_PDF