On Mar 10, 2006, at 3:18 AM, Paul Rehill wrote:
One more question. Do you have a good function for the inverse of the
standard normal cumulative distribution?
Function InvCumNormDist(p as Double, Mean as Double = 0.0, StdDev as
Double = 1.0) As Double
Const a1= -3.969683028665376e+01
Const a2= 2.209460984245205e+02
Const a3= -2.759285104469687e+02
Const a4= 1.383577518672690e+02
Const a5= -3.066479806614716e+01
Const a6= 2.506628277459239e+00
Const b1= -5.447609879822406e+01
Const b2= 1.615858368580409e+02
Const b3= -1.556989798598866e+02
Const b4= 6.680131188771972e+01
Const b5= -1.328068155288572e+01
Const c1= -7.784894002430293e-03
Const c2= -3.223964580411365e-01
Const c3= -2.400758277161838e+00
Const c4= -2.549732539343734e+00
Const c5= 4.374664141464968e+00
Const c6= 2.938163982698783e+00
Const d1= 7.784695709041462e-03
Const d2= 3.224671290700398e-01
Const d3= 2.445134137142996e+00
Const d4= 3.754408661907416e+00
Const Sqrt_2Pi = 2.5066282746310
Const p_low = 0.02425
Const p_high= 0.97575
Dim z, r as Double
if p < 0.0 or p >= 1.0 Then Return - 1
if p < p_low then
z = Sqrt(-2.0*Ln(p))
z = (((((c1*z+c2)*z+c3)*z+c4)*z+c5)*z+c6) / ((((d1*z+d2)*z+d3)*z
+d4)*z+1.0)
elseif p <= p_high then
z = p - 0.5
r = z*z
z = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r+a6)*z /(((((b1*r+b2)*r+b3)
*r+b4)*r+b5)*r+1.0)
else
z = Sqrt(-2.0*Ln(1.0-p))
z = -(((((c1*z+c2)*z+c3)*z+c4)*z+c5)*z+c6) /((((d1*z+d2)*z+d3)*z
+d4)*z+1.0)
End if
r = (CumNormalDist(z) - p) * Sqrt_2Pi * Exp(0.5 * z*z)
z = z - ( r/(1+0.5*z*r))
return mean + z*StdDev
End Function
'-----------------------------------------------------------------------
-------------------
Function CumNormalDist(Z as Double, Mean as Double = 0.0, StdDev as
Double = 1.0) As Double
Const a1 = 0.31938153
Const a2 = -0.356563782
Const a3 = 1.781477937
Const a4 = -1.821255978
Const a5 = 1.330274429
Const Sqrt_2Pi = 2.5066282746310
Dim K, w As double , isNegative as boolean
z = (z - Mean)/StdDev
if z < 0.0 then
isNegative = true
z = Abs(z)
End if
K = 1.0 / (1.0 + 0.2316419 * z)
w= 1.0 - 1.0 /Sqrt_2Pi * Exp(-z * z / 2.0) * (a1 * K + a2 * K*K +
a3 * Pow(K, 3) + a4 * Pow(K , 4) + a5 * Pow(K, 5))
If isNegative Then w = 1.0 - w
Return w
End Function
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