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IMSL_FCDF

IMSL_FCDF

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

This routine requires an IDL Advanced Math and Stats license. For more information, contact your 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.

Example


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 (optional)

If present and nonzero, double precision is used.

INVERSE (optional)

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



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