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