{ RCSid $Id: norm.cal,v 1.4 2021/09/12 17:04:41 greg Exp $ }
{
	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) ;

{ ### Old approximation:

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

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

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

### erf() gives us exact value: }

Q(u) : .5 - .5*erf(u/sqrt(2)) ;

u2(t) : t - (2.515517+t*(.802853+t*.010328))/
		(1+t*(1.432788+t*(.189269+t*.001308))) ;

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

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