MODULE DE FONCTIONS STATISTIQUES EN VB6

' L'algorithme du codage de la loi inverse du Chi-deux provient de la traduction d'un code source
' en JavaScript sur le site internet suivant :
'   http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html

	'The following JavaScript functions for calculating normal and
	'chi-square probabilities and critical values were adapted by
	'John Walker from C implementations
	'written by Gary Perlman of Wang Institute, Tyngsboro, MA 01879.
	'Both the original C code and this JavaScript edition
	'are in the public domain.



'Public Const Pi = 3.14159265359




'densité de probabilité de la loi normale centrée réduite
Function PHI(ByVal u As Double) As Double
    PHI = (1 / ((2 * Pi) ^ 0.5)) * Exp(-0.5 * (u ^ 2))
End Function



'Fonction de la table inverse de la loi normale centrée réduite
Function NORMAL(ByVal p As Double) As Double

    Dim xo, xx, y, h, f, f1, f2, fd, r, s As Double
    Dim N, i, k As Integer
    xo = 0.5
    y = 0
    xx = xo
    N = 200
    'Suite convergente de Newton
    Do While Abs(xx - y) > 0.00001
        y = xx
        h = 2 * xx / N
        f1 = 0
        f2 = 0
        'Résolution d'une intégrale numérique
        For i = 0 To ((N - 2) / 2)
            r = -xx + 2 * i * h
            s = -xx + (2 * i + 1) * h
            If i = 0 Then
                f1 = f1 + 0
                f2 = f2 + PHI(s)
            Else
                f1 = f1 + PHI(r)
                f2 = f2 + PHI(s)
            End If
        Next
        f = (h / 3) * (PHI(-xx) + PHI(xx) + 2 * f1 + 4 * f2) - p
        fd = 2 * PHI(xx)
        xx = xx - f / fd
    Loop
    NORMAL = xx
    
End Function



' Renvoie la probabilité d'une variable aléatoire z suivant la loi normale centrée réduite
Function poz(ByVal z As Double) As Double
'POZ  --  probability of normal z value

'Adapted from a polynomial approximation in:
'Ibbetson D, Algorithm 209
'Collected Algorithms of the CACM 1963 p. 616

'Note:
    'This routine has six digit accuracy, so it is only useful for absolute
    'z values < 6.  For z values >= to 6.0, poz() returns 0.0.
    
    
    Dim y, x, w As Double
    Dim z_max As Double
    z_max = 6
    If z = 0 Then
        x = 0
    Else
        y = 0.5 * Abs(z)
        If y >= z_max * 0.5 Then
            x = 1
        ElseIf y < 1 Then
            w = y * y
            x = ((((((((0.000124818987 * w - 0.001075204047) * w _
                    + 0.005198775019) * w - 0.019198292004) * w _
                    + 0.059054035642) * w - 0.151968751364) * w _
                    + 0.319152932694) * w - 0.5319230073) * w _
                    + 0.797884560593) * y * 2
        Else
            y = y - 2
            x = (((((((((((((-0.000045255659 * y + 0.00015252929) * y _
                    - 0.000019538132) * y - 0.000676904986) * y _
                    + 0.001390604284) * y - 0.00079462082) * y _
                    - 0.002034254874) * y + 0.006549791214) * y _
                    - 0.010557625006) * y + 0.011630447319) * y _
                    - 0.009279453341) * y + 0.005353579108) * y _
                    - 0.002141268741) * y + 0.000535310849) * y _
                    + 0.999936657524
        End If
    End If
    If z > 0 Then
        poz = ((x + 1) * 0.5)
    Else
        poz = ((1 - x) * 0.5)
    End If
    Dim bigx As Double
    bigx = 20
    
End Function




Function pochisq(ByVal x As Double, ByVal df As Integer) As Double
' Adapted From:
'Hill, I. D. and Pike, M. C.  Algorithm 299
'Collected Algorithms for the CACM 1967 p. 243
'Updated for rounding errors based on remark in
'ACM TOMS June 1985, page 185
    
    Dim a, y, s, e, c, v As Double
    Dim even As Boolean
    'even correspond à la parité de df, le degré de liberté
    Dim lnpi, ipi As Double
    lnpi = Log(Pi ^ 0.5)
    ipi = 1 / Log(Pi)
    If ((x <= 0) Or (df < 1)) Then
        pochisq = 1
    End If
    a = 0.5 * x
    If Fix(df / 2) = df / 2 Then
        even = True
    Else
        even = False
    End If
    If df > 1 Then
        y = Exp(-a)
    End If
    If even = True Then
        s = y
    Else
        s = 2 * poz(-(x ^ 0.5))
    End If
    If df > 2 Then
        x = 0.5 * (df - 1)
        If even = True Then
            z = 1
        Else
            z = 0.5
        End If
        If (a > bigx) Then
            If even = True Then
                e = 0
            Else
                e = lnpi
            End If
            
            c = Log(a)
            
            Do While (z <= x)
                e = Log(z) + e
                s = s + Exp(c * z - a - e)
                z = z + 1
            Loop
            pochisq = s
        Else
            If even = True Then
                e = 1
            Else
                e = ipi / (a ^ 0.5)
            End If
            c = 0
            Do While (z <= x)
                e = e * (a / z)
                c = c + e
                z = z + 1
            Loop
            pochisq = c * y + s
        End If
    Else
        pochisq = s
    End If
    
End Function


Function critchi(ByVal p As Double, ByVal df As Integer) As Double

    Dim epsilon, chimax, minchisq, maxchisq, chisqval As Double
    epsilon = 0.000001
    chimax = 99999
    minchisq = 0
    maxchisq = chimax
    If p <= 0 Then
        critchi = maxchisq
    Else
        If p >= 1 Then
            critchi = 0
        End If
    End If
    chisqval = df / (p ^ 0.5)
    Do While ((maxchisq - minchisq) > epsilon)
        If (pochisq(chisqval, df) < p) Then
            maxchisq = chisqval
        Else
            minchisq = chisqval
        End If
        chisqval = (maxchisq + minchisq) * 0.5
    Loop
    critchi = chisqval
    
End Function

'renvoie, pour la probabilité p et le degré de liberté df, la variable
Function invchi2(ByVal p As Double, ByVal df As Double) As Double

    invchi2 = critchi(p, df)
    
End Function

'renvoie, pour la variable x et le degré de liberté df, la probabilité
Function chi2(ByVal x As Double, ByVal df As Integer) As Double

    chi2 = pochisq(x, df)
    
End Function