cal/cal/norm.cal

{
        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(log(1/p/p))) ;

u2(t) = t - (2.515517+t*(.802853+t*.010328))/
                (1+t*(1.432788+t*(.189269+t*.001308))) ;
Revision:	1.1
Committed:	Sat Feb 22 02:07:21 2003 UTC (21 years, 2 months ago) by greg
Branch:	MAIN
CVS Tags:	rad3R7P2, rad3R7P1, rad4R1, rad4R0, rad3R5, rad3R6, rad3R6P1, rad3R8, rad3R9
Log Message:	Changes and check-in for 3.5 release Includes new source files and modifications not recorded for many years See ray/doc/notes/ReleaseNotes for notes between 3.1 and 3.5 release
#	Content
1	{
2	Normal Distribution Functions
3
4	10/20/87
5
6	Z(u) - normal probability density function
7
8	Q(u) - Z(u) integrated from u to infinity
9
10	u(p) - u for known value p = Q(u)
11	}
12
13	NORMF : 1/sqrt(2*PI) ;
14
15	Z(u) = NORMF * exp(-u*u/2) ;
16
17	Q(u) = if( u, Q1(u), 1-Q1(-u) ) ;
18
19	Q1(u) = Z(u) * Q2(1/(1+.2316419*u)) ;
20
21	Q2(t) = t(.31938153+t(-.356563782+t*(1.781477937+
22	t(-1.821255978+t1.330274429)))) ;
23
24	u(p) = if( .5-p, u1(p), -u1(1-p) ) ;
25
26	u1(p) = u2(sqrt(log(1/p/p))) ;
27
28	u2(t) = t - (2.515517+t(.802853+t.010328))/
29	(1+t(1.432788+t(.189269+t*.001308))) ;