TNIN

This function evaluates the inverse of the noncentral Student’s t cumulative distribution function.

Function Return Value

TNIN — Function value. (Output)
The probability that a noncentral Student’s t random variable takes a value less than or equal to TNIN is P.

Required Arguments

P — Probability for which the inverse of the noncentral Student’s t cumulative distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).

IDF — Number of degrees of freedom of the noncentral Student’s t cumulative distribution. (Input) IDF must be positive.

DELTA — The noncentrality parameter. (Input)

FORTRAN 90 Interface

Generic: TNIN (P, IDF, DELTA)

Specific: The specific interface names are S_TNIN and D_TNIN.

FORTRAN 77 Interface

Single: TNIN (P, IDF, DELTA)

Double: The double precision name is DTNIN.

Description

Function TNIN evaluates the inverse distribution function of a noncentral t random variable with IDF degrees of freedom and noncentrality parameter DELTA; that is, with P = P, ν = IDF, and δ = DELTA, it determines t0 (= TNIN(P,IDF,DELTA )), such that

 

where Γ(⋅) is the gamma function. The probability that the random variable takes a value less than or equal to t0 is P. See TNDF for an alternative definition in terms of normal and chi‑squared random variables. The function TNIN uses bisection and modified regula falsi to invert the distribution function, which is evaluated using routine TNDF.

Comments

Informational Error

 

Type

Code

Description

4

1

Over 100 iterations have occurred without convergence. Convergence is assumed.

Example

In this example, we find the 95‑th percentage point for a noncentral t random variable with 6 degrees of freedom and noncentrality parameter 6.

 

USE TNIN_INT

USE UMACH_INT

IMPLICIT NONE

INTEGER IDF, NOUT

REAL DELTA, P, T

!

CALL UMACH (2, NOUT)

IDF = 6

DELTA = 6.0

P = 0.95

T = TNIN(P,IDF,DELTA)

WRITE (NOUT,99999) T

!

99999 FORMAT (' The 0.05 noncentral t critical value is ', F6.3, &

'.')

!

END

Output

 

The 0.05 noncentral t critical value is 11.995.