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_FIN and D_FIN.

FORTRAN 77 Interface

Single: FIN (P, DFN, DFD)

Double: The double precision name is DFIN.

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