FCDF Function

Evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.

Usage

result = FCDF(f, dfnum, dfden)

Input Parameters

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

dfnum—Numerator degrees of freedom. Parameter dfnum must be positive.

dfden—Denominator degrees of freedom. Parameter dfden must be positive.

Returned Value

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

Input 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).

Discussion

Function FCDF 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 n₁ and n₂ degrees of freedom and Y = (n₁X)/(n₂ + n₁X), then Y is a beta variate with parameters p = n₁/2 and q = n₂/2. The FCDF function also uses a relationship between F random variables that is expressed as follows: F_F(f, n₁, n₂) = 1 – F_F(1/f, n₂, n₁), where F_F is the distribution function for an F random variable.

If Inverse is specified, the FCDF function evaluates the inverse distribution function of a Snedecor’s F random variable with n₁ = dfnum numerator degrees of freedom and n₂ = 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 - FCDF(f, 1, 1)

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

   'variate is greater than 648 is:'

; PV-WAVE prints the following:

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

; 0.0249959

Fatal Errors

STAT_F_INVERSE_OVERFLOW—Function 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.