Gamma 分布，不完整的 beta 函数
Gamma distribution, incomplete beta function
我需要计算 Gamma 累积分布，这似乎与计算不完整的 beta 函数相当。
Excel 确实有一个包含的计算器，但我没有发现使用过的算法的痕迹。
你们中有人知道计算此函数的准确方法吗？
我尝试了以下内容，从网站翻译成 VB.NET，但它给出了愚蠢的结果：
Function IncompleteBetaFunc(x As Double, a As Double, b As Double) As Double
If x <= 0 Or x >= 1 Then Return 0
Dim bt As Double
bt = Math.Exp(GammaLn(a + b) - GammaLn(a) - GammaLn(b) + a * Math.Log(x) + b * Math.Log(1.0 - x))
If x < (a + 1.0) / (a + b + 2.0) Then
Return bt * betacf(a, b, x) / a
Else
Return 1.0 - bt * betacf(b, a, 1.0 - x) / b
End If
End Function
Function betacf(x As Double, a As Double, b As Double) As Double
Const MAXIT As Integer = 100
Const EPS As Double = 0.0000003
Const FPMIN As Double = 1.0E-30
Dim aa, c, d, del, h, qab, qam, qap As Double
Dim m, m2 As Integer
qab = a + b
qap = a + 1.0
qam = a - 1.0
c = 1.0
d = 1.0 - qab * x / qap
If (Math.Abs(d) < FPMIN) Then d = FPMIN
d = 1.0 / d
h = d
For m = 1 To MAXIT
m2 = 2 * m
aa = m * (b - m) * x / ((qam + m2) * (a + m2))
d = 1.0 + aa * d
If (Math.Abs(d) < FPMIN) Then d = FPMIN
c = 1.0 + aa / c
If (Math.Abs(c) < FPMIN) Then c = FPMIN
d = 1.0 / d
h *= d * c
aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2))
d = 1.0 + aa * d
If (Math.Abs(d) < FPMIN) Then d = FPMIN
c = 1.0 + aa / c
If (Math.Abs(c) < FPMIN) Then c = FPMIN
d = 1.0 / d
del = d * c
h *= del
If (Math.Abs(del - 1.0) < EPS) Then Exit For
Next
Return h
End Function
谢谢！
Meta.Numerics includes well-tested and performant code for this any many other special functions. Its incomplete Beta function is documented here. The underlying code can be studied here. It also has a full-on Gamma distribution object, which will give moments, generate random variates, and do other distribution-related stuff in addition to computing the CDF. The package available via NuGet；只需在 VS NuGet 界面中搜索 Meta.Numerics。
我需要计算 Gamma 累积分布，这似乎与计算不完整的 beta 函数相当。 Excel 确实有一个包含的计算器，但我没有发现使用过的算法的痕迹。 你们中有人知道计算此函数的准确方法吗？ 我尝试了以下内容，从网站翻译成 VB.NET，但它给出了愚蠢的结果：
Function IncompleteBetaFunc(x As Double, a As Double, b As Double) As Double
If x <= 0 Or x >= 1 Then Return 0
Dim bt As Double
bt = Math.Exp(GammaLn(a + b) - GammaLn(a) - GammaLn(b) + a * Math.Log(x) + b * Math.Log(1.0 - x))
If x < (a + 1.0) / (a + b + 2.0) Then
Return bt * betacf(a, b, x) / a
Else
Return 1.0 - bt * betacf(b, a, 1.0 - x) / b
End If
End Function
Function betacf(x As Double, a As Double, b As Double) As Double
Const MAXIT As Integer = 100
Const EPS As Double = 0.0000003
Const FPMIN As Double = 1.0E-30
Dim aa, c, d, del, h, qab, qam, qap As Double
Dim m, m2 As Integer
qab = a + b
qap = a + 1.0
qam = a - 1.0
c = 1.0
d = 1.0 - qab * x / qap
If (Math.Abs(d) < FPMIN) Then d = FPMIN
d = 1.0 / d
h = d
For m = 1 To MAXIT
m2 = 2 * m
aa = m * (b - m) * x / ((qam + m2) * (a + m2))
d = 1.0 + aa * d
If (Math.Abs(d) < FPMIN) Then d = FPMIN
c = 1.0 + aa / c
If (Math.Abs(c) < FPMIN) Then c = FPMIN
d = 1.0 / d
h *= d * c
aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2))
d = 1.0 + aa * d
If (Math.Abs(d) < FPMIN) Then d = FPMIN
c = 1.0 + aa / c
If (Math.Abs(c) < FPMIN) Then c = FPMIN
d = 1.0 / d
del = d * c
h *= del
If (Math.Abs(del - 1.0) < EPS) Then Exit For
Next
Return h
End Function
谢谢！
Meta.Numerics includes well-tested and performant code for this any many other special functions. Its incomplete Beta function is documented here. The underlying code can be studied here. It also has a full-on Gamma distribution object, which will give moments, generate random variates, and do other distribution-related stuff in addition to computing the CDF. The package available via NuGet；只需在 VS NuGet 界面中搜索 Meta.Numerics。