Expression 14: "C" left parenthesis, "x" , right parenthesis equals 1 half ( 1 plus "E" Subscript, "r" "f" , Baseline ( StartFraction, ln "x" minus "b" Over "a" StartRoot, 2 , EndRoot , EndFraction ) )Cx=12(1+Erf(lnx−ba2))
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Complementary Log-Normal CDF:
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Expression 16: "C" Subscript, "C" , Baseline left parenthesis, "x" , right parenthesis equals 1 minus "C" left parenthesis, "x" , right parenthesisCCx=1−Cx
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erf() using Abramowitz and Stegun formula 7.1.26 (error < 1.5e-7)
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Expression 18: "E" Subscript, "r" "f" , Baseline left parenthesis, "x" , right parenthesis equals signum left parenthesis, "x" , right parenthesis left parenthesis, 1 minus left parenthesis, left parenthesis, left parenthesis, left parenthesis, left parenthesis, 1.0 6 1 4 0 5 4 2 9 times "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis plus negative 1.4 5 3 1 5 2 0 2 7 , right parenthesis times "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis plus 1.4 2 1 4 1 3 7 4 1 , right parenthesis times "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis plus negative 0.2 8 4 4 9 6 7 3 6 , right parenthesis times "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis plus 0.2 5 4 8 2 9 5 9 2 , right parenthesis times "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis times exp left parenthesis, negative left parenthesis, "x" times "x" , right parenthesis , right parenthesis , right parenthesisErfx=signx1−1.061405429·tASx+−1.453152027·tASx+1.421413741·tASx+−0.284496736·tASx+0.254829592·tASx·exp−x·x
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Expression 19: "t" Subscript, "A" "S" , Baseline left parenthesis, "x" , right parenthesis equals StartFraction, 1 Over 1 plus 0.3 2 7 5 9 1 1abs left parenthesis, "x" , right parenthesis , EndFractiontASx=11+0.3275911absx
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Color in the 3 Lighthouse scoring buckets
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Expression 21: 1 greater than "y" greater than or equal to .9 01>y≥.90
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Expression 22: .9 0 greater than "y" greater than or equal to .5 0.90>y≥.50
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Expression 23: .5 0 greater than "y" greater than 0.50>y>0
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Plot the control points
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podr: left parenthesis, "p" , 1 minus "C" left parenthesis, "p" , right parenthesis , right parenthesisp,1−Cp
Label:
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median: left parenthesis, "m" , 1 minus "C" left parenthesis, "m" , right parenthesis , right parenthesism,1−Cm