TIN
This function evaluates the inverse of the Student’s t cumulative distribution function.
Function Return Value
TIN — Function value. (Output)
The probability that a Student’s t random variable takes a value less than or equal to TIN is P.
Required Arguments
P — Probability for which the inverse of the Student’s t cumulative distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).
DF — Degrees of freedom. (Input)
DF must be greater than or equal to 1.0.
FORTRAN 90 Interface
Generic: TIN (P, DF)
Specific: The specific interface names are S_TIN and D_TIN.
FORTRAN 77 Interface
Single: TIN (P, DF)
Double: The double precision name is DTIN.
Description
Function
TIN evaluates the inverse distribution function of a Student’s
t random variable with
DF degrees of freedom. Let
ν =
DF. If
ν equals 1 or 2, the inverse can be obtained in closed form, if
ν is between 1 and 2, the relationship of a
t to a beta random variable is exploited and routine
BETIN is used to evaluate the inverse; otherwise the algorithm of Hill (1970) is used. For small values of
ν greater than 2, Hill’s algorithm inverts an integrated expansion in 1/(1 +
t2/
ν) of the
t density. For larger values, an asymptotic inverse Cornish‑Fisher type expansion about normal deviates is used.
Comments
Informational error
Type | Code | Description |
|---|
4 | 3 | TIN 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 β distribution. |
Example
In this example, we find the 0.05 critical value for a two‑sided t test with 6 degrees of freedom.
USE TIN_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER NOUT
REAL DF, P, T
!
CALL UMACH (2, NOUT)
P = 0.975
DF = 6.0
T = TIN(P,DF)
WRITE (NOUT,99999) T
99999 FORMAT (' The two-sided t(6) 0.05 critical value is ', F6.3)
END
Output
The two-sided t(6) 0.05 critical value is 2.447
