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greg |
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{ RCSid $Id: norm.cal,v 1.3 2017/04/19 22:09:12 greg Exp $ } |
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greg |
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{ |
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Normal Distribution Functions |
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10/20/87 |
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Z(u) - normal probability density function |
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Q(u) - Z(u) integrated from u to infinity |
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u(p) - u for known value p = Q(u) |
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} |
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NORMF : 1/sqrt(2*PI) ; |
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greg |
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Z(u) : NORMF * exp(-u*u/2) ; |
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greg |
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greg |
1.4 |
{ ### Old approximation: |
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greg |
1.3 |
Q2(t) : t*(.31938153+t*(-.356563782+t*(1.781477937+ |
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t*(-1.821255978+t*1.330274429)))) ; |
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greg |
1.1 |
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greg |
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Q1(u) : Z(u) * Q2(1/(1+.2316419*u)) ; |
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greg |
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greg |
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Q(u) : if( u, Q1(u), 1-Q1(-u) ) ; |
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greg |
1.1 |
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greg |
1.4 |
### erf() gives us exact value: } |
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Q(u) : .5 - .5*erf(u/sqrt(2)) ; |
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greg |
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u2(t) : t - (2.515517+t*(.802853+t*.010328))/ |
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(1+t*(1.432788+t*(.189269+t*.001308))) ; |
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greg |
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greg |
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u1(p) : u2(sqrt(-2*log(p))) ; |
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greg |
1.1 |
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greg |
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u(p) : if( .5-p, u1(p), -u1(1-p) ) ; |
