cal/cal/norm.cal

{ RCSid $Id$ }
{
        Normal Distribution Functions

                10/20/87

        Z(u)            - normal probability density function

        Q(u)            - Z(u) integrated from u to infinity

        u(p)            - u for known value p = Q(u)
}

NORMF : 1/sqrt(2*PI) ;

Z(u) = NORMF * exp(-u*u/2) ;

Q(u) = if( u, Q1(u), 1-Q1(-u) ) ;

Q1(u) = Z(u) * Q2(1/(1+.2316419*u)) ;

Q2(t) = t*(.31938153+t*(-.356563782+t*(1.781477937+
                t*(-1.821255978+t*1.330274429)))) ;

u(p) = if( .5-p, u1(p), -u1(1-p) ) ;

u1(p) = u2(sqrt(-2*log(p))) ;

u2(t) = t - (2.515517+t*(.802853+t*.010328))/
                (1+t*(1.432788+t*(.189269+t*.001308))) ;
Revision:	1.2
Committed:	Wed Apr 25 01:06:25 2012 UTC (12 years ago) by greg
Branch:	MAIN
CVS Tags:	rad4R2P2, rad5R0, rad4R2, rad4R2P1
Changes since 1.1:	+2 -1 lines
Log Message:	Simplified expression
#	User	Rev	Content
1	greg	1.2	{ RCSid $Id$ }
2	greg	1.1	{
3			Normal Distribution Functions
4
5			10/20/87
6
7			Z(u) - normal probability density function
8
9			Q(u) - Z(u) integrated from u to infinity
10
11			u(p) - u for known value p = Q(u)
12			}
13
14			NORMF : 1/sqrt(2*PI) ;
15
16			Z(u) = NORMF * exp(-u*u/2) ;
17
18			Q(u) = if( u, Q1(u), 1-Q1(-u) ) ;
19
20			Q1(u) = Z(u) * Q2(1/(1+.2316419*u)) ;
21
22			Q2(t) = t(.31938153+t(-.356563782+t*(1.781477937+
23			t(-1.821255978+t1.330274429)))) ;
24
25			u(p) = if( .5-p, u1(p), -u1(1-p) ) ;
26
27	greg	1.2	u1(p) = u2(sqrt(-2*log(p))) ;
28	greg	1.1
29			u2(t) = t - (2.515517+t(.802853+t.010328))/
30			(1+t(1.432788+t(.189269+t*.001308))) ;