Expression 14: "C" left parenthesis, "x" , right parenthesis equals 1 half ( 1 minus "E" Subscript, "r" "f" , Baseline ( StartFraction, ln "x" minus mu Over StartRoot, 2 , EndRoot sigma , EndFraction ) )Cx=12(1−Erf(lnx−μ2σ))
14
p = old "point of diminishing returns" control point
15
Expression 16: "p" equals exponent left parenthesis, mu plus StartFraction, sigma Over 2 , EndFraction left parenthesis, negative 3 sigma minus StartRoot, 4 plus sigma squared , EndRoot , right parenthesis , right parenthesisp=expμ+σ2−3σ−4+σ2
equals=
2499.3 1 6 7 4 5 62499.3167456
16
erf() using Abramowitz and Stegun formula 7.1.26 (error < 1.5e-7)
17
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
18
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
19
Color in the 3 Lighthouse scoring buckets
20
Expression 21: 1 greater than "y" greater than or equal to .9 01>y≥.90
21
Expression 22: .9 0 greater than "y" greater than or equal to .5 0.90>y≥.50
22
Expression 23: .5 0 greater than "y" greater than 0.50>y>0
23
Plot the control points
24
podr: left parenthesis, "p" , "C" left parenthesis, "p" , right parenthesis , right parenthesisp,Cp
Label:
25
median: left parenthesis, "m" , "C" left parenthesis, "m" , right parenthesis , right parenthesism,Cm
Label:
26
p10: left parenthesis, "p" Subscript, 10 , Baseline , "C" left parenthesis, "p" Subscript, 10 , Baseline , right parenthesis , right parenthesisp10,Cp10