G101 Inverse of Chi-Square Distribution

Function subprogram CHISIN calculates $\chi 2(P,N)$ for a given probability $P(\chi 2)$ and a given degree of freedom N, where

$P(\chi 2|N)\; =\; \{12N\Gamma (\{12\}N)\}\int$₀^χ2(P,N) e^-{12}tt^{12}N-1 dt

and $N\; \ge 1$ and .

Structure:

FUNCTION subprogram
User Entry Name: CHISIN
Files Referenced: Unit 6
External References: GAUSIN (G105), MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, CHISIN(P,N) has the value $\chi 2(P,N)$ ,

where CHISIN and P are of type REAL, and N is of type INTEGER.

Method:

The method is described in Ref. 1. Note that there the complementary integral is taken.

Accuracy:

Approximately three to six digits are correct. The case N = 3 is the least accurate.

Error handling:

Error G101.1: or $P\; \ge 1$ .
Error G101.2: .
In both cases, the function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

This subprogram is based on an Algol60 procedure published in Ref. 1.

References:

1. R.B. Goldstein, Algorithm 451, Chi-Square Quantiles, Collected Algorithms from CACM (1972)

G102