FIN
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
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. 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 | Description |
|---|
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
