G100: Upper Tail Probability of Chi-Squared Distribution

Author(s): G. Folger, K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 21.08.1971
Language: Fortran	Revised: 15.01.1994

Function subprogram PROB computes the probability that a random variable having a -distribution with degrees of freedom assumes a value which is larger than a given value , i.e.

Structure:

FUNCTION subprogram
User Entry Names: PROB
External References: ERFC, DERFC, MTLMTR, ABEND

Usage:

In any arithmetic expression,

PROB(X,N) has the value .

PROB and X are of type REAL and N is of type INTEGER.

Method:

See Ref. 1, formulae Nr. 26.4.4, 26.4.5 and, for N>300, No. 26.4.14.

Accuracy:

For , PROB has an accuracy of about six digits. For , the accuracy decreases for with increasing X.

Error handling:

Error G100.1: .
Error G100.2: .
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.

References:

1. M. Abramowitz and I.A. Stegun (eds.), Handbook of mathematical functions with formulas, graphs, and mathematcal tables, 9th printing with corrections, (Dover, New York 1972).