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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))) ;
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