CSNIN

This function evaluates the inverse of the noncentral chi‑squared cumulative function.

Function Return Value

CSNIN — Function value. (Output)
The probability that a noncentral chi‑squared random variable takes a value less than or equal to CSNIN is P.

Required Arguments

P — Probability for which the inverse of the noncentral chi‑squared cumulative distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).

DF — Number of degrees of freedom of the noncentral chi‑squared distribution. (Input)
DF must be greater than or equal to 0.5 and less than or equal to 200,000.

ALAM — The noncentrality parameter. (Input)
ALAM must be nonnegative, and ALAM + DF must be less than or equal to 200,000.

FORTRAN 90 Interface

Generic: CSNIN (P, DF, ALAM)

Specific: The specific interface names are S_CSNIN and D_CSNIN.

FORTRAN 77 Interface

Single: CSNIN (P, DF, ALAM)

Double: The double precision name is DCSNIN.

Description

Function CSNIN evaluates the inverse distribution function of a noncentral chi‑squared random variable with DF degrees of freedom and noncentrality parameter ALAM; that is, with P = P, v = DF, and =λ = ALAM, it determines c0 (= CSNIN(P,DF,ALAM)), such that

 

where Γ(⋅) is the gamma function. The probability that the random variable takes a value less than or equal to c0 is P .

Function CSNIN uses bisection and modified regula falsi to invert the distribution function, which is evaluated using routine CSNDF. See CSNDF for an alternative definition of the noncentral chi‑squared random variable in terms of normal random variables.

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 chi‑squared random variable with 2 degrees of freedom and noncentrality parameter 1.

 

USE CSNIN_INT

USE UMACH_INT

IMPLICIT NONE

INTEGER NOUT

REAL ALAM, CHSQ, DF, P

!

CALL UMACH (2, NOUT)

DF = 2.0

ALAM = 1.0

P = 0.95

CHSQ = CSNIN(P,DF,ALAM)

WRITE (NOUT,99999) CHSQ

!

99999 FORMAT (' The 0.05 noncentral chi-squared critical value is ', &

F6.3, '.')

!

END

Output

 

The 0.05 noncentral chi-squared critical value is 8.642.