This function evaluates the inverse of the F cumulative distribution function.
Function Return Value
FIN — Function
value. (Output)
The probability that an F random variable
takes a value less than or equal to FIN is P.
Required Arguments
P — Probability
for which the inverse of the F distribution function is to be
evaluated. (Input)
P must be in the open
interval (0.0, 1.0).
DFN — Numerator
degrees of freedom. (Input)
DFN must be
positive.
DFD — Denominator
degrees of freedom. (Input)
DFD must be
positive.
FORTRAN 90 Interface
Generic: FIN (P, DFN, DFD)
Specific: The specific interface names are S_FDF and D_FDF.
FORTRAN 77 Interface
Single: FIN (P, DFN, DFD)
Double: The double precision name is DFDF.
Description
Function FIN evaluates the inverse distribution function of a Snedecor's F random variable with DFN numerator degrees of freedom and DFD denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then using the routine BETIN. If X is an F variate with v1 and v2 degrees of freedom and Y = v1X/(v2 + v1X), then Y is a beta variate with parameters p = v1/2 and q = v2/2. If P ≤ 0.5, FIN uses this relationship directly, otherwise, it also uses a relationship between F random variables that can be expressed as follows, using routine FDF, which is the F cumulative distribution function:
FDF(F, DFN, DFD) = 1.0 − FDF(1.0/F, DFD, DFN).
Comments
Informational error
Type Code
4 4 FIN 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.
Example
In this example, we find the 99-th percentage point for an F random variable with 1 and 7 degrees of freedom.
USE UMACH_INT
USE FIN_INT
IMPLICIT NONE
INTEGER NOUT
REAL DFD, DFN, F, P
!
CALL UMACH (2, NOUT)
P = 0.99
DFN = 1.0
DFD = 7.0
F = FIN(P,DFN,DFD)
WRITE (NOUT,99999) F
99999 FORMAT (' The F(1,7) 0.01 critical value is ', F6.3)
END
Output
The F(1, 7) 0.01 critical value is 12.246
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