G105 Inverse of Normal Frequency Function

Function subprograms GAUSIN and DGAUSN calculate the inverse $X(P)$ of the normal frequency function (Gaussian distribution)

$P(X)\; =\; \{12\pi \}\int$_-&inf;^X(P)e^-{12}t2dt

for real arguments P, where 0 < P < 1.

Structure:

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

Usage:

In any arithmetic expression, GAUSIN(P) has the value $X(P)$ ,

where GAUSIN and P are of type REAL.

Method:

The method is described in Ref. 1.

Accuracy:

Accuracy:

GAUSIN (except on CDC and Cray computers) has an accuracy of about six digits. For most values of the argument P, DGAUSN (and GAUSIN on CDC and Cray computers) has an accuracy of approximately one significant digit less than the machine precision.

Error handling:

Error G105.1: $P\; \le 0$ or $P\; \ge 1$ .
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. G.W. Hill and A.W. Davis, Algorithm 442, Normal Deviate, Collected Algorithms from CACM (1973)

G106