COMPLEMENTARY_F_CDF Function

Evaluates the complement of the F distribution function.

Usage

result = COMPLEMENTARY_F_CDF (f, df_numerator, df_denominator)

Input Parameters

f—Scalar float value for which Pr(x > f) is to be evaluated.

df_numerator—Scalar float value indicating the numerator degrees of freedom. df_numerator must be positive.

df_denominator—Scalar float value indicating the denominator degrees of freedom. df_denominator must be positive.

Returned Value

result—The probability that an F random variable takes a value greater than f.

Input Keywords

Double—If present and nonzero, then double precision is used.

Discussion

COMPLEMENTARY_F_CDF evaluates one minus the distribution function of a Snedecor’s F random variable with df_numerator and df_denominator. The function is evaluated by making a transformation to a beta random variable, 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. COMPLEMENTARY_F_CDF also uses a relationship between F random variables that can be expressed as:

F_F(f, n₁, n₂) = F_F(1/f, n₂, n₁)

where F_F is the distribution function for an F random variable.

This function provides higher right tail accuracy for the F distribution.

 

Plot of F_F (f, df_n, df_d)

Example

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

PRO t_complementary_f_cdf_ex1

    F = 648.0

    df_numerator = 1.0

    df_denominator = 1.0 

    p = COMPLEMENTARY_F_CDF(F,df_numerator, df_denominator)

    PRINT,"The probability that an F(", $

          STRTRIM(STRING(df_numerator,Format="(f3.1)"),2),",",$

          STRTRIM(STRING(df_denominator,Format="(f3.1)"),2),$

          ") variate is greater than ", $

          STRING(F,Format="(f5.1)")," is ",$

          STRING(p,Format="(f6.4)")

END

Output

The probability that an F(1.0,1.0) variate is greater than 648.0 

is 0.0250.