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% 计算不完全Beta函数. % 参考文献: % 何光渝.《Visual Basic 应用数值算法集》[M].北京:科学出版社,170－171,2002. function Incmp_Beta_Result=IncmpBeta(a,b,X) [m n]=size(X); aaa=Gammln(a+b)-Gammln(a)-Gammln(b); for i=1:m for j=1:n if X(i,j)<0 | X(i,j)>1 helpdlg('变量X的取值范围不在0和1之间','错误！'); return end if X(i,j)==0 | X(i,j)==1 bt(i,j)=0; else bt(i,j)=exp(aaa+a*log(X(i,j))+b*log(1-X(i,j))); end end end for i=1:m for j=1:n if X(i,j)<((a+1)/(a+b+2)) Incmp_Beta_Result(i,j)=bt(i,j)*Betacf(a,b,X(i,j))/a; else Incmp_Beta_Result(i,j)=1-bt(i,j)*Betacf(b,a,1-X(i,j))/b; end end end %//////////////Betacf过程////////////////////////////// function Betacf_Result=Betacf(a,b,x) itmax=100; eps=0.0000003; am=1; bm=1; az=1; qab=a+b; qap=a+1; qam=a-1; bz=1-qab*x/qap; for m=1:itmax em=m; tem=em+em; d=em*(b-m)*x/((qam+tem)*(a+tem)); ap=az+d*am; bp=bz+d*bm; d=-(a+em)*(qab+em)*x/((a+tem)*(qap+tem)); aap=ap+d*az; bpp=bp+d*bz; aold=az; am=ap/bpp; bm=bp/bpp; az=aap/bpp; bz=1; if abs(az-aold)<eps*abs(az) Betacf_Result=az; break; end end Betacf_Result=az; %/////////////计算gama函数程序//////////////////////// function Gammln_result=Gammln(xx) 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=1.0; fpf=5.5; x=xx-one; tmp=x+fpf; tmp=(x+half)*log(tmp)-tmp; ser=one; for j=1:6 x=x+one; ser=ser+cof(j)./x; end Gammln_result=tmp+log(stp*ser); %----------programs end here---------------