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.
