# IMSL_FCDF

The IMSL_FCDF function evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.

Note: This routine requires an IDL Analyst license. For more information, contact your Exelis VIS sales or technical support representative.

The IMSL_FCDF function evaluates the distribution function of a Snedecor’s F random variable with dfnum and dfden. The function is evaluated by making a transformation to a beta random variable and then evaluating the incomplete beta function. If X is an F variate with ν1 and ν2 degrees of freedom and Y = (ν1X)/(ν2 + ν1X), then Y is a beta variate with parameters p = ν1/2 and q = ν2/2. The IMSL_FCDF function also uses a relationship between F random variables that is expressed as follows: FF(f, ν1, ν2) = 1 – FF(1/f, ν2, ν1), where FF is the distribution function for an F random variable.

If INVERSE is specified, the IMSL_FCDF function evaluates the inverse distribution function of a Snedecor’s F random variable with ν1 = dfnum numerator degrees of freedom and ν2 = dfden denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then evaluating the inverse of an incomplete beta function.

## Examples

### Example 1

This example finds the probability that an F random variable with one numerator and one denominator degree of freedom is greater than 648.

f = 648

p = 1 - IMSL_FCDF(f, 1, 1)

PM, p, Title = 'The probability that an F(1,1) ' + $

'variate is greater than 648 is:'

The probability that an F(1,1) variate is greater than 648 is:

0.0249959

## Syntax

Result = IMSL_FCDF(f, dfnum, dfden [, /DOUBLE] [, /INVERSE] )

## Return Value

The probability that an F random variable takes a value less than or equal to the input point f.

## Arguments

### dfden

Denominator degrees of freedom. Parameter dfden must be positive.

### dfnum

Numerator degrees of freedom. Parameter dfnum must be positive.

### f

Expression for which the F distribution function is to be evaluated.

## Keywords

### DOUBLE

If present and nonzero, double precision is used.

### INVERSE

If present and nonzero, evaluates the inverse of the F distribution function. If inverse is specified, argument f represents the probability for which the inverse of the F distribution function is to be evaluated. In this case, f must be in the open interval (0.0, 1.0).

## Errors

### Fatal Errors

`STAT_F_INVERSE_OVERFLOW` - IMSL_FCDF is set to machine infinity since overflow would occur upon modifying the inverse value for the F distribution with the result obtained from the inverse beta distribution.

## Version History

6.4 | Introduced

## See Also