matlab里面q函数,Matlab 高斯 Chi方 右尾函数 Q函数

function [P]=Qchipr2(nu,lambda,x,epsilon)

%

% This program computes the right-tail probability

% of a central or noncentral chi-squared PDF.

%

% Input Parameters:

%

% nu = Degrees of freedom (1,2,3,etc.)

%

% lambda = Noncentrality parameter (must be positive),

% set = 0 for central chi-squared PDF

% x Real vector value of random variable

% epsilon = maximum allowable error (should be a small

% number such as 1e-5) due to truncation of the

% infinite sum

%

% Output Parameters:

%

% P = right-tail probability or probability that

% the random variable exceeds the given value

% (1 - CDF)

%

% Verification Test Case:

%

% The inputs nu=1, lambda=2, x=0.5, epsilon=0.0001

% should produce P=0.7772

% The inputs nu=5, lambda=6, x=10, epsilon=0.0001

% should produce P=0.5063

% The inputs nu=8, lambda=10, x=15, epsilon=0.0001

% should produce P=0.6161

%

% Determin how many terms in sum to be used (find M)

t=exp(lambda/2)*(1-epsilon);

sum=1;

M=0;

while sum

M=M+1;

sum=sum+((lambda/2)^M)/prod(1:M);

end

% Use different algorithm for nu even or odd.

if (nu/2-floor(nu/2)) == 0 % nu is even.

% Compute k=0 term of sum.

% compute Qchi2_nu((x).

% Start recursion with Qchi2_2(x).

Q2=exp(-x/2);g=Q2;

for m=4:2:nu % If nu=2 , loop will be omitted.

g=g.*x/(m-2);

Q2=Q2+g;

end

% Finish computation of k=0 term.

P=exp(-lambda/2)*Q2;

% Compute remaining terms of sum.

for k=1:M

m=nu+2*k;

g=g.*x/(m-2);Q2=Q2+g;

arg=(exp(-lambda/2)*(lambda/2)^k)/prod(1:k);

P=P+arg*Q2;

end

else % nu is odd

% Compute k=0 term of sum.

P=2*Q(sqrt(x));

% Start recursion with Qchi2p_3(x).

Q2p=sqrt(2*x/pi).*exp(-x/2);g=Q2p;

if nu >1

for m=5:2:nu % If nu=3 , loop will be omitted

g=g.*x/(m-2);

Q2p=Q2p+g;

end

P=exp(-lambda/2)*Q2p;

% Compute remaining terms of sum.

for k=1:M

m=nu+2*k;

g=g.*x/(m-2);Q2p=Q2p+g;

arg=(exp(-lambda/2)*(lambda/2)^k)/prod(1:k);

P=P+arg*Q2p;

end

else

% If nu=1, the k=0 term is just Qchi2_1(x)=2Q(sqrt(x)).

% Add the k=0 and k=1 terms.

P=P+exp(-lambda/2)*(lambda/2)*Q2p;

% Compute remaining terms.

for k=2:M

m=nu+2*k;

g=g.*x/(m-2);Q2p=Q2p+g;

arg=(exp(-lambda/2)*(lambda/2)^k)/prod(1:k);

P=P+arg*Q2p;

end

end

end

end

function y=Q(x)

y=0.5*erfc(x/sqrt(2));

end

function y=Qinv(x)

y=sqrt(2)*erfinv(1-2*x);

end

normcdf

norminv

chi2cdf

chi2inv

ncx2cdf

ncx2inv