t分布分位数m.bas

<VB数理统计实用算法>书中的算法源程序

Attribute VB_Name = "modMethod"
Option Explicit
'求t分布的分位数
'n：自由度，已知
'Q：上侧概率（<=0.5），已知
'T：分位数，所求
Public Sub PT_DIST(n As Integer, Q As Double, T As Double)
    Dim PIS As Double, DFR2 As Double, C As Double
    Dim Q2 As Double, p As Double, YQ As Double, E As Double
    Dim GA1 As Double, GA2 As Double, GA3 As Double
    Dim T0 As Double, pp As Double, d As Double
    Dim K As Integer
    Const PI As Double = 3.14159265359
    PIS = Sqr(PI): DFR2 = n / 2
    If n = 1 Then
        T = Tan(PI * (0.5 - Q)): Exit Sub
    End If
    If n = 2 Then
        If Q > 0.5 Then C = -1 Else C = 1
        Q2 = (1 - 2 * Q) ^ 2
        T = Sqr(2 * Q2 / (1 - Q2)) * C
        Exit Sub
    End If
    p = 1 - Q: PNorm Q, YQ              '正态分布分位数
    E = (1 - 1 / (4 * n)) ^ 2 - YQ * YQ / (2 * n)
    If E > 0.5 Then
        T0 = YQ / Sqr(E)
    Else
        lnGamma DFR2, GA1: lnGamma DFR2 + 0.5, GA2
        GA3 = Exp((GA1 - GA2) / n)
        T0 = Sqr(n) / (PIS * Q * n) ^ (1 / n) / GA3
    End If
    For K = 1 To 30
        T_Dist n, T0, pp, d
        If d = 0 Then
            T = T0: Exit Sub
        End If
        T = T0 - (pp - p) / d
        If Abs(T0 - T) < 0.000001 * Abs(T) Then _
            Exit Sub Else T0 = T
    Next K
End Sub

'计算GAMMA函数
'x：自变量
'z：GAMMA函数值
Public Sub GAMMA(x As Double, z As Double)
    Dim H As Double, y As Double, y1 As Double
    H = 1: y = x
LL1:
    If y = 2 Then
        z = H
        Exit Sub
    ElseIf y < 2 Then
        H = H / y: y = y + 1: GoTo LL1
    ElseIf y >= 3 Then
        y = y - 1: H = H * y: GoTo LL1
    End If
    y = y - 2
    y1 = y * (0.005159 + y * 0.001606)
    y1 = y * (0.004451 + y1)
    y1 = y * (0.07211 + y1)
    y1 = y * (0.082112 + y1)
    y1 = y * (0.41174 + y1)
    y1 = y * (0.422787 + y1)
    H = H * (0.999999 + y1)
    z = H
End Sub

'求Gamma函数的对数LogGamma(x)
'x：自变量
'G：Gamma函数的对数
Public Sub lnGamma(x As Double, G As Double)
    Dim y As Double, z As Double, A As Double
    Dim b As Double, b1 As Double, n As Integer
    Dim I As Integer
    If x < 8 Then
        y = x + 8: n = -1
    Else
        y = x: n = 1
    End If
    z = 1 / (y * y)
    A = (y - 0.5) * Log(y) - y + 0.9189385
    b1 = (0.0007663452 * z - 0.0005940956) * z
    b1 = (b1 + 0.0007936431) * z
    b1 = (b1 - 0.002777778) * z
    b = (b1 + 0.0833333) / y
    G = A + b
    If n >= 0 Then Exit Sub
    y = y - 1: A = y
    For I = 1 To 7
        A = A * (y - I)
    Next I
    G = G - Log(A)
End Sub

'求正态分布的分位数
'Q：上侧概率
'x：分位数
Public Sub PNorm(Q, x)
    Dim p As Double, y As Double, z As Double
    Dim b0 As Double, b1 As Double, b2 As Double
    Dim b3 As Double, b4 As Double, b5 As Double
    Dim b6 As Double, b7 As Double, b8 As Double
    Dim b9 As Double, b10 As Double, b As Double
    b0 = 1.570796288
    b1 = 0.03706987906
    b2 = -0.0008364353589
    b3 = -0.0002250947176
    b4 = 0.000006841218299
    b5 = 0.000005824238515
    b6 = -0.00000104527497
    b7 = 8.360937017E-08
    b8 = -3.231081277E-09
    b9 = 3.657763036E-11
    b10 = 6.936233982E-13
    If Q = 0.5 Then
        x = 0: GoTo PN01
    End If
    If Q > 0.5 Then p = 1 - Q Else p = Q
    y = -Log(4 * p * (1 - p))
    b = y * (b9 + y * b10)
    b = y * (b8 + b)
    b = y * (b7 + b)
    b = y * (b6 + b)
    b = y * (b5 + b)
    b = y * (b4 + b)
    b = y * (b3 + b)
    b = y * (b2 + b)
    b = y * (b1 + b)
    z = y * (b0 + b)
    x = Sqr(z)
    If Q > 0.5 Then x = -x
PN01:
End Sub

'计算t分布的分布函数
'n：自由度，已知
'T：t值，已知
'pp：下侧概率，所求
'dd：概率密度，所求
Public Sub T_Dist(n As Integer, T As Double, pp As Double, dd As Double)
    Dim Sign As Integer, TT As Double, x As Double
    Dim p As Double, u As Double, GA1 As Double, GA2 As Double
    Dim IBI As Integer, N2 As Integer, I As Integer
    Const PI As Double = 3.14159265359
    If T = 0 Then
        Call GAMMA(n / 2, GA1): Call GAMMA(n / 2 + 0.5, GA2): pp = 0.5
        dd = GA2 / (Sqr(n * PI) * GA1): Exit Sub
    End If
    If T < 0 Then Sign = -1 Else Sign = 1
    TT = T * T: x = TT / (n + TT)
    If (n \ 2) * 2 = n Then                 'n为偶数
        p = Sqr(x): u = p * (1 - x) / 2
        IBI = 2
    Else                                    'n为奇数
        u = Sqr(x * (1 - x)) / PI
        p = 1 - 2 * Atn(Sqr((1 - x) / x)) / PI
        IBI = 1
    End If
    If IBI = n Then GoTo LL1 Else N2 = n - 2
    For I = IBI To N2 Step 2
        p = p + 2 * u / I
        u = u * (1 + I) / I * (1 - x)
    Next I
LL1:
    dd = u / Abs(T)
    pp = 0.5 + Sign * p / 2
End Sub