java调用Excel中的GAMMADIST函数返回伽玛分布
java调用Excel中的GAMMADIST函数返回伽玛分布
一、问题描述:想用java调用Excel中的GAMMADIST 函数。
Microsoft office Excel中用法说明如下：https://support.microsoft.com/zh-cn/office/gammadist-%E5%87%BD%E6%95%B0-7327c94d-0f05-4511-83df-1dd7ed23e19e?ui=zh-cn&rs=zh-cn&ad=cn
WPS Excel中用法说明如下：https://www.wps.cn/learning/room/d/328021
二、尝试网上找的vb版GammaDist()和GammaInv()两函数的代码转java
1、从matlab里翻译过来的vb版GammaDist()和GammaInv()两函数的代码如下：
vb版GammaDist()和GammaInv()两函数的代码
http://wenku.baidu.com/link?url=uHtUUETc8q1HAlSV7ChTHRg0SLrBKApRKC-BLFnHHoviqv3G4r4DY8ONIWi_5fKN6DuBURHhAkOfJvGNJg7mFyjjERKRoeWASkFTmK3yvXa从matlab里翻译过来的
GammaDist(x,a,b,true):
'%GAMCDF Gamma cumulative distribution function.
'% P = GAMCDF(X,A,B) returns the gamma cumulative distribution
'% function with parameters A and B at the values in X.
Public Function GamCdf(x, a, b)
'对应excel中GammaDist(x,a,b,true)函数,
计算S曲线
If a <= 0 Or b <= 0 Then GammCdf = "NaN"
GamCdf = GAMMAINC(x / b, a)
p = IIf(p > 1, 1, p)
End Function
'%GAMMAINC Incomplete gamma function.
'% Y = GAMMAINC(X,A) evaluates the incomplete gamma function for
'% corresponding elements of X and A. X and A must be real and the same
'% size (or either can be a scalar). A must also be non-negative.
'% The incomplete gamma function is defined as:
'%gammainc(x,a) = 1 ./ gamma(a) .*
'% integral from 0 to x of t^(a-1) exp(-t) dt
'% '% For any a>=0, as x approaches infinity, gammainc(x,a) approaches 1.
'% For small x and a, gammainc(x,a) ~= x^a, so gammainc(0,0) = 1.
Public Function GAMMAINC(x, a)
Dim amax As Double
amax = 2 ^ 20
ascalar = 1
If a <= amax Then
If a <> 0 And x <> 0 And x < a + 1 Then
xk = x
ak = a
ap = ak
Sum = 1 / ap
del = Sum
Dim i As Double
For i = 1 To 10000
ap = ap + 1
del = xk * del / ap
Sum = Sum + del
Next
GAMMAINC = Sum * Exp(-xk + ak * Log(xk) - GAMMALN(ak))
ElseIf a <> 0 And x <> 0 And x >= a + 1 Then
xk = x
a0 = 1
a1 = x
b0 = 0
b1 = a0
ak = a
fac = 1
n = 1
g = b1
gold = b0
For i = 1 To 10000
gold = g
ana = n - ak
a0 = (a1 + a0 * ana) * fac
b0 = (b1 + b0 * ana) * fac
anf = n * fac
a1 = xk * a0 + anf * a1
b1 = xk * b0 + anf * b1
fac = 1 / a1
g = b1 * fac
n = n + 1
Next
GAMMAINC = 1 - Exp(-xk + ak * Log(xk) - GAMMALN(ak)) * g
End If
Else
End If
End Function
'*****************************************************************************************************
**************
'%GAMMALN Logarithm of gamma function.
'%
Y = GAMMALN(X) computes the natural logarithm of the gamma
'% function for each element of X. GAMMALN is defined as
'% '% LOG(GAMMA(X))
'% '% and is obtained without computing GAMMA(X). Since the gamma
'% function can range over very large or very small values, its
'% logarithm is sometimes more useful. http://zanjero.ygblog.com/
Public Function GAMMALN(XX)
Dim COF(6) As Double, stp As Double, half As Double, one As Double
Dim fpf As Double, x As Double, tmp As Double, ser As Double
Dim j As Integer
COF(1) = 76.18009173
COF(2) = -86.50532033
COF(3) = 24.01409822
COF(4) = -1.231739516
COF(5) = 0.00120858003
COF(6) = -0.00000536382
stp = 2.50662827465
half = 0.5
one = 1#
fpf = 5.5
x = XX - one
tmp = x + fpf
tmp = (x + half) * Log(tmp) - tmp
ser = one
For j = 1 To 6
x = x + one
ser = ser + COF(j) / x
Next j
GAMMALN = tmp + Log(stp * ser)
End Function
GammaInv:(要调用上面的GamCdf和GAMMALN函数)
'%GAMINV Inverse of the gamma cumulative distribution function (cdf).
'% X = GAMINV(P,A,B) returns the inverse of the gamma cdf with
'% parameters A and B, at the probabilities in P对应Excel中GammaInv(p,a,b)函数，计算PⅢ的Φp值Φp＝Cs/2*GammaInv(1-p/100,4/Cs^2,1)-2/Cs
Public Function gaminv(p, a, b)
If p < 0 Or p > 1 Or a <= 0 Or b <= 0 Then
gaminv = "NaN"
Exit Function
Else
Select Case p
Case 0
gaminv = 0
Case 1
gaminv = 1
Case Else
'% Newton's Method
'% Permit no more than count_limit interations.
count_limit = 100
cunt = 0
pk = p
'% Supply a starting guess for the iteration.
'% Use a method of moments fit to the lognormal distribution.
mn = a * b
v = mn * b
temp = Log(v + mn ^ 2)
mu = 2 * Log(mn) - 0.5 * temp
sigma = -2 * Log(mn) + temp
xk = Exp(MyNormInv(pk, mu, sigma))
'''''''''''''''''''''''
h = 1
'% Break out of the iteration loop for three reasons:
'% 1) the last update is very small (compared to x)
'% 2) the last update is very small (compared to sqrt(eps))
'% 3) There are more than 100 iterations. This should NEVER happen.
eps = 2 ^ -10
Do While Abs(h) > eps ^ 0.5 * Abs(xk) And Abs(h) > eps ^ 0.5 And cunt < count_limit
cunt = tunt + 1
h = (GamCdf(xk, a, b) - pk) / gampdf(xk, a, b)
'''''''''''''
xnew = xk - h
% Make sure that the current guess stays greater than zero.
% When Newton's Method suggests steps that lead to negative guesses
% take a step 9/10ths of the way to zero:
If xnew < 0 Then
xnew = xk / 10
h = xk - xnew
End If
xk = xnew
Loop
gaminv = xk
End Select
End If
End Function
' This function is a replacement for the Microsoft Excel Worksheet function NORMSINV.
' It uses the algorithm of Peter J. Acklam to compute the inverse normal cumulative
' distribution. Refer to
http://home.online.no/~pjacklam/notes/invnorm/index.html
for
' a description of the algorithm.
' Adapted to VB by Christian d'Heureuse,
http://zanjero.ygblog.com/.
Public Function MyNormSInv(ByVal p As Double)
'
计算频率格纸
Const a1 = -39.6968302866538, a2 = 220.946098424521, a3 = -275.928510446969
Const a4 = 138.357751867269, a5 = -30.6647980661472, a6 = 2.50662827745924
Const b1 = -54.4760987982241, b2 = 161.585836858041, b3 = -155.698979859887
Const b4 = 66.8013118877197, b5 = -13.2806815528857, c1 = -7.78489400243029E-03
Const c2 = -0.322396458041136, c3 = -2.40075827716184, c4 = -2.54973253934373
Const c5 = 4.37466414146497, c6 = 2.93816398269878, d1 = 7.78469570904146E-03
Const d2 = 0.32246712907004, d3 = 2.445134137143, d4 = 3.75440866190742
Const p_low = 0.02425, p_high = 1 - p_low
Dim q As Double, r As Double
If p < 0 Or p > 1 Then
Err.Raise vbObjectError, , "NormSInv: Argument out of range."
ElseIf p < p_low Then
q = Sqr(-2 * Log(p))
MyNormSInv = (((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / _
((((d1 * q + d2) * q + d3) * q + d4) * q + 1)
ElseIf p <= p_high Then
q = p - 0.5: r = q * q
MyNormSInv = (((((a1 * r + a2) * r + a3) * r + a4) * r + a5) * r + a6) * q / _
(((((b1 * r + b2) * r + b3) * r + b4) * r + b5) * r + 1)
Else
q = Sqr(-2 * Log(1 - p))
MyNormSInv = -(((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / _
((((d1 * q + d2) * q + d3) * q + d4) * q + 1)
End If
End Function
'%GAMPDF Gamma probability density function.
'%
Y = GAMPDF(X,A,B) returns the gamma probability density function
'%
with parameters A and B, at the values in X.
http://zanjero.ygblog.com/
Public Function gampdf(x, a, b)
y = 0
If x = 0 And a < 1 Then
gampdf = "∞"
Exit Function
End If
If x = 0 And a = 1 Then
gampdf = 1 / b
Exit Function
End If
If a <= 0 Or b <= 0 Then
y = "NaN"
gampdf = y
Exit Function
ElseIf x > 0 Then
y = (a - 1) * Log(x) - x / b - GAMMALN(a) - a * Log(b)
y = Exp(y)
End If
gampdf = y
End Function
https://wenku.baidu.com/link?url=uHtUUETc8q1HAlSV7ChTHRg0SLrBKApRKC-BLFnHHoviqv3G4r4DY8ONIWi_5fKN6DuBURHhAkOfJvGNJg7mFyjjERKRoeWASkFTmK3yvXa&_wkts_=1667896077426
https://bbs.co188.com/thread-1169888-1-1.html
2、转成java后代码如下：
import static java.lang.Double.NEGATIVE_INFINITY; //无穷小
import static java.lang.Double.POSITIVE_INFINITY; //无穷大
import static java.lang.Math.*;
public class GammaDist {
//对应excel中GammaDist(x,a,b,true)函数,
public GammaDist(double x,double a,double b, boolean flag){
if(flag){
double p = GamCdf(x,a,b);
if(p>1)
p=1;
else
p=p;
System.out.println (p);
}
}
//%GAMCDF Gamma cumulative distribution function.
//% P = GAMCDF(X,A,B) returns the gamma cumulative distribution
//% function with parameters A and B at the values in X.
public double GamCdf(double x, double a, double b) { //对应excel中GammaDist(x,a,b,true)函数,计算S曲线
double GamCdf = NEGATIVE_INFINITY; //无穷小
if(a<=0 || b<=0) GamCdf = NEGATIVE_INFINITY; //无穷小
GamCdf = GAMMAINC(x / b, a);
double p = GamCdf;
if(p>1)
p=1;
else
p=p;
return GamCdf;
}
//%GAMMAINC Incomplete gamma function.
//% Y = GAMMAINC(X,A) evaluates the incomplete gamma function for
//% corresponding elements of X and A.X and A must be real and the same
//% size (or either can be a scalar).A must also be non-negative.
//% The incomplete gamma function is defined as: http://zanjero.ygblog.com
//%gammainc(x,a) = 1 ./ gamma(a) .*
//%integral from 0 to x of t^(a-1) exp(-t) dt
//% For any a>=0, as x approaches infinity, gammainc(x,a) approaches 1.
//% For small x and a, gammainc(x,a) ~= x^a, so gammainc(0,0) = 1.
public double GAMMAINC(double x, double a) {
double amax;
amax = Math.pow(2,20);
int ascalar = 1;
double GAMMAINC = 0.0;
if(a <=amax) {
if (a != 0 && x != 0 && x < a + 1) {
double xk = x;
double ak = a;
double ap = ak;
double Sum = 1 / ap;
double del = Sum;
for (int i = 0; i < 10000; i++) {
ap = ap + 1;
del = xk * del / ap;
Sum = Sum + del;
}
GAMMAINC = Sum * exp(-xk + ak * log(xk) - GAMMALN(ak));
}
else if (a != 0 && x != 0 && x >= a + 1) {
double xk = x;
double a0 = 1;
double a1 = x;
double b0 = 0;
double b1 = a0;
double ak = a;
double fac = 1;
double n = 1;
double g = b1;
double gold = b0;
for (int i = 0; i < 10000; i++) {
gold = g;
double ana = n - ak;
a0 = (a1 + a0 * ana) * fac;
b0 = (b1 + b0 * ana) * fac;
double anf = n * fac;
a1 = xk * a0 + anf * a1;
b1 = xk * b0 + anf * b1;
fac = 1 / a1;
g = b1 * fac;
n = n + 1;
}
GAMMAINC = 1 - exp(-xk + ak * log(xk) - GAMMALN(ak)) * g;
}
}
return GAMMAINC;
}
//'*****************************************************************************************************
//**************
//%GAMMALN Logarithm of gamma function.
//%Y = GAMMALN(X) computes the natural logarithm of the gamma
//% function for each element of X.GAMMALN is defined as
//% '%LOG(GAMMA(X))
//% '% and is obtained without computing GAMMA(X).Since the gamma
//% function can range over very large or very small values, its
//% logarithm is sometimes more useful.http://zanjero.ygblog.com/
public double GAMMALN( double XX) {
double[] COF = new double[6];
double stp, half, one;
double fpf, x, tmp, ser;
COF[0] = 76.18009173;
COF[1] = -86.50532033;
COF[2] = 24.01409822;
COF[3] = -1.231739516;
COF[4] = 0.00120858003;
COF[5] = -0.00000536382;
stp = 2.50662827465;
half = 0.5;
one = 1;
fpf = 5.5;
x = XX - one;
tmp = x + fpf;
tmp = (x + half) * log(tmp) - tmp;
ser = one;
for(int j=0;j<6;j++) {
x = x + one;
ser = ser + COF[j] / x;
}
double GAMMALN = tmp + log(stp * ser);
return GAMMALN;
}
//GammaInv:(要调用上面的GamCdf和GAMMALN函数)
//%GAMINV Inverse of the gamma cumulative distribution function (cdf).
//% X = GAMINV(P,A,B)returns the inverse of the gamma cdf with
//% parameters A and B, at the probabilities in P. http://zanjero.ygblog.com/
//% 对应Excel中GammaInv(p,a,b)函数，计算PⅢ的Φp值Φp＝Cs/2*GammaInv(1-p/100,4/Cs^2,1)-2/Cs
public double gaminv(double p, double a, double b) {
double gaminv = NEGATIVE_INFINITY;//无穷小
if(p <0 || p >1 || a <= 0 || b <= 0) {
gaminv = NEGATIVE_INFINITY;//无穷小
return gaminv;
}
else {
if(p==0){
gaminv = 0;
}
else if(p==1){
gaminv = 1;
}
else {
//% Newton' s Method
//% Permit no more than count_limit interations.
int count_limit = 100;
int cunt = 0;
double pk = p;
//% Supply a starting guess for the iteration.
//% Use a method of moments fit to the lognormal distribution.
double mn = a * b;
double v = mn * b;
double temp = log(v + Math.pow(mn,2));
double mu = 2 * log(mn) - 0.5 * temp;
double sigma = -2 * log(mn) + temp;
double xk = exp(MyNormInv(pk, mu, sigma));
//'' '' '' '' '' '' '' '' '' '' '' '
double h = 1;
//% Break out of the iteration loop for three reasons:
//%1) the last update is very small (compared to x)
//%2) the last update is very small (compared to sqrt(eps))
//%3) There are more than 100 iterations. This should NEVER happen.
double eps = Math.pow(2,-10);
while((abs(h) > Math.pow(eps,0.5) * abs(xk)) && (abs (h) > Math.pow(eps,0.5)) && (cunt 1) {
System.out.println ("NormSInv: Argument out of range.");
}
else if( p 0) {
y = (a - 1) * log(x) - x / b - GAMMALN(a) - a * log(b);
y = exp(y);
}
gampdf = y;
return gampdf;
}
}
3、结论，转换未成功，函数MyNormInv和变量tunt未找到，有知道的请留言告知。
三、最后使用org.apache.commons.math3.distribution.GammaDistribution类中的方法成功。参考地址：https://vimsky.com/examples/detail/java-class-org.apache.commons.math3.distribution.GammaDistribution.html