related to error function

[amit saraf]

How to find inverse of complementary error and error function

 

[Argy - Arcasoft]

Hummm? Please refrase or expand your question.

Argy

 

[Dana DeLouis]

How to find inverse of complementary error and error function

Hi. If you don't get a better solution, here is a Newton version
of the Inverse Error function. The normal Series equation converges too
slowly in my opinion.
Note that Excel's ERF() function can't work with Negative values (it's a
known bug). This tries to work around it.
As a simple test, we try to get back the same values...

Sub TestIt()
Debug.Print InverseERF([Erf(.1)])
Debug.Print InverseERF([Erf(.9)])
Debug.Print InverseERF([Erf(2)])
Debug.Print InverseERF([-Erf(2)])
End Sub


Function InverseERF(N)
Dim J As Long 'Counter
Dim G As Double 'Guess
Dim Ng As Double 'New Guess
Dim K As Double 'Constant
Dim M As Double 'Hold Positive value of n

Select Case N
Case -1
InverseERF = "-Infinity"
Case 1
InverseERF = "+Infinity"
Case -1 To 1
'Valid
With WorksheetFunction
K = [SqrtPi(1)/2]
Ng = 0.5
M = Abs(N)
Do
G = Ng
Ng = G + K * Exp(G * G) * (.ErfC(G) + M - 1)
J = J + 1
Loop While G <> Ng And J < 30
'It's a Odd function, so ok.
InverseERF = Sgn(N) * Ng
End With
Case Else
InverseERF = "Invalid"
End Select
End Function

- - -
HTH
Dana DeLouis

 

[shg]

You can use these, with a reference to atpvbaen.

Code:
--------------------
' The worksheet ERF and ERFC functions only allow non-negative
' arguments less than about 27.334, although the mathematical functions are valid
' across the domain of Reals. The ERF function reaches its asymptotic limit of 1
' (to double precision accuracy) by 5.8

' The functions myERF and myERFC are identical in interface to the worksheet
' functions, but work for any value of the arguments.

Function myERF(a As Double, Optional b As Variant)
myERF = myERF1(a)
If Not IsMissing(b) Then myERF = myERF1(CDbl(b)) - myERF
End Function

Function myERFC(x As Double) As Double
myERFC = 1# - myERF(x)
End Function

Private Function myERF1(x As Double) As Double
If Abs(x) > 5.8 Then
myERF1 = Sgn(x)
ElseIf x <> 0 Then
myERF1 = Sgn(x) * Application.Run("ATPVBAEN.XLA!ERF", Abs(x))
End If
End Function

 

[Jerry W. Lewis]

Use the relationship between these functions and functions for which Excel
does have inverses.
ERF(x) = GAMMADIST(x^2,0.5,1,TRUE)
ERFC(x) = 2*NORMSDIST(-x*SQRT(2)) = CHIDIST(2*x^2,1)
so
invERF(p) = SQRT(GAMMAINV(p,0.5,1))
invERFC(p) = -NORMSINV(p/2)/SQRT(2) = SQRT(CHIINV(p,1)/2)

For Excel 2003 or later, NORMSDIST and NORMSINV are much more accurate than
ERFC for large values of x. For earlier versions of Excel, CHIDIST is more
accurate than ERFC, but neither inverse function performs well for large x
(small p).

Jerry