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{ RCSid $Id: normcomp.cal,v 1.4 2021/09/12 17:04:41 greg Exp $ } |
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{ |
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Compute overlap between two normal distribution functions, |
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defined by mean1, mean2, stdev1 and stdev2. |
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2/10/95 Greg Ward |
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relies on gauss.cal and norm.cal |
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} |
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Z1(u) = Z((u - mean1)/stdev1) / stdev1; |
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Z2(u) = Z((u - mean2)/stdev2) / stdev2; |
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f(u) = min(Z1(u),Z2(u)); |
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xmin = min(mean1-3*stdev1, mean2-3*stdev2); |
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xmax = max(mean1+3*stdev1, mean2+3*stdev2); |
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{ |
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Following is an alternative calculation that doesn't |
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require numerical integration, nor gauss.cal nor norm.cal |
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(ref: stats.stackexchange.com/questions/103800 – wolfies Dec 24 '16 at 14:40) |
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} |
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abs(x) : if(x, x, -x); |
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Finteg(c, m, s) : 0.5*erf((c-m)/(sqrt(2)*s)); |
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m1 = mean1; m2 = mean2; |
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s1 = stdev1; s2 = stdev2; |
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den = s1*s1 - s2*s2; |
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c0 = (m2*s1*s1 - m1*s2*s2)/den; |
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cr = s1*s2*sqrt((m1-m2)*(m1-m2) + 2*den*log(s1/s2))/den; |
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NormOverlap = if(1e-7 - abs(s1-s2), erfc(abs(m1-m2)/(s1+s2)/sqrt(2)), |
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1 - Finteg(c0-cr,m1,s1) + Finteg(c0-cr,m2,s2) |
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+ Finteg(c0+cr,m1,s1) - Finteg(c0+cr,m2,s2) ); |
