Iman Conover (Excel / VBA)

Thu, 14 May 2026 10:41:00 +0100

“When your work speaks for itself, don’t interrupt.” [Henry J. Kaiser]

Abstract

Falls Sie korrelierte Zufallszahlen erzeugen müssen, ist die Iman Conover Methode besser als die Cholesky Zerlegung.

1982 veröffentlichten Iman und Conover ihren ursprünglichen Artikel (externer Link!) “A distribution-free approach to inducing rank correlation among input variables”.

Rick Wicklin schrieb dazu im Jahr 2021 (externer Link!) “Simulate correlated variables by using the Iman-Conover transformation”. Sein Artikel enthält eine SAS Implementierung der Iman Conover Methode.

Cholesky (VBA)

Thu, 14 May 2026 02:46:00 +0100

Abstract

Mit der Cholesky (sprich: “Koleski”) Zerlegung können Sie einfach korrelierte Zufallszahlen erzeugen. Ich stelle hier ein einfaches Beispiel vor. Den besseren Iman Conover Ansatz finden Sie hier.

Appendix – Programmcode Cholesky und RandCorr

Bitte den Haftungsausschluss im Impressum beachten.

Function Cholesky(vA As Variant) As Variant
'I suggest to use the Cholesky decomposition just for purposes of demonstration.
'Better options are (in this order): tred2, tqli, eigsrt from Numerical Recipes.
'SVD also works but is computationally more expensive by far since it does not
'make use of symmetry.
'(Thanks to my former colleague Glen R.)
'Source (EN): https://www.sulprobil.de/cholesky_en/
'Source (DE): https://www.berndplumhoff.de/cholesky_de/
'Bernd Plumhoff 02-Nov-2024 PB V1.1
Dim d As Double
Dim i As Long, j As Long, k As Long, n As Long
With Application.WorksheetFunction
On Error Resume Next
vA = .Transpose(.Transpose(vA))
On Error GoTo 0
n = UBound(vA, 1)
If n <> UBound(vA, 2) Then
  Cholesky = CVErr(xlErrRef)
  Exit Function
End If

ReDim dR(1 To n, 1 To n) As Double 'Zeroing all elements
For j = 1 To n
  d = 0#
  For k = 1 To j - 1
    d = d + dR(j, k) * dR(j, k)
  Next k
  dR(j, j) = vA(j, j) - d
  If dR(j, j) > 0# Then
    dR(j, j) = Sqr(dR(j, j))
    For i = j + 1 To n
      d = 0#
      For k = 1 To j - 1
        d = d + dR(i, k) * dR(j, k)
      Next k
      dR(i, j) = (vA(i, j) - d) / dR(j, j)
    Next i
  Else
    'Cannot continue with usual Cholesky
    'Fill this column with zeros. Idea: Glen R.
    For i = j To n
      dR(i, j) = 0#
    Next i
  End If
Next j
Cholesky = dR
End With
End Function

Function RandCorr(n As Long, vVarCovar As Variant) As Variant
'Returns Ubound(vVarCovar,1) correlated random number vectors of length n.
'vVarCovar is a square matrix containing the variance/covariance matrix.
'Please notice that you will only get a "proxy" correlation, not an exact one.
'Bernd Plumhoff 06-Nov-2009 PB V0.2
Dim vA As Variant
Dim d As Double
Dim i As Long, j As Long, k As Long, m As Long

With Application.WorksheetFunction
vA = .Transpose(.Transpose(vVarCovar))
m = UBound(vA, 1)
If m <> UBound(vA, 2) Then
  RandCorr = CVErr(xlErrRef)
  Exit Function
End If

ReDim Db(1 To m, 1 To m) As Double
For j = 1 To m
  d = 0#
  For k = 1 To j - 1
    d = d + Db(j, k) * Db(j, k)
  Next k
  Db(j, j) = vA(j, j) - d
  If Db(j, j) <= 0 Then
    RandCorr = CVErr(xlErrNum)
    Exit Function
  End If
  Db(j, j) = Sqr(Db(j, j))
  
  For i = j + 1 To m
    d = 0#
    For k = 1 To j - 1
      d = d + Db(i, k) * Db(j, k)
    Next k
    Db(i, j) = (vA(i, j) - d) / Db(j, j)
  Next i
Next j

ReDim vR(1 To n, 1 To m) As Variant
For i = 1 To n
  For j = 1 To m
    vR(i, j) = .Norm_S_Inv(Rnd())
  Next j
Next i
vR = .MMult(vR, Db)
RandCorr = vR
End With
End Function

Downlaod

Bitte den Haftungsausschluss im Impressum beachten.

Cholesky Matrix on Bernd Plumhoff

Iman Conover (Excel / VBA)

Abstract

Cholesky (VBA)

Abstract

Appendix – Programmcode Cholesky und RandCorr

Downlaod