54 lines
1.2 KiB
Matlab
54 lines
1.2 KiB
Matlab
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% bivmom.m Date: 1/11/2004
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% This Matlab program computes the product moment of X_1^{p_1}X_2^{p_2},
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% where X_1 and X_2 are standard bivariate normally distributed.
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% n : dimension of X
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% rho: correlation coefficient between X_1 and X_2
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% Reference: Kotz, Balakrishnan, and Johnson (2000), Continuous Multivariate
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% Distributions, Vol. 1, p.261
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% Note that there is a typo in Eq.(46.25), there should be an extra rho in front
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% of the equation.
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% Usage: bivmom(p,rho)
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%
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function [y,dy] = bivmom(p,rho)
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s1 = p(1);
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s2 = p(2);
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rho2 = rho^2;
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if nargout > 1
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drho2 = 2*rho;
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end
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if rem(s1+s2,2)==1
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y = 0;
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return
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end
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r = fix(s1/2);
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s = fix(s2/2);
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y = 1;
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c = 1;
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if nargout > 1
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dy = 0;
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dc = 0;
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end
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odd = 2*rem(s1,2);
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for j=1:min(r,s)
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if nargout > 1
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dc = 2*dc*(r+1-j)*(s+1-j)*rho2/(j*(2*j-1+odd)) + 2*c*(r+1-j)*(s+1-j)*drho2/(j*(2*j-1+odd));
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end
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c = 2*c*(r+1-j)*(s+1-j)*rho2/(j*(2*j-1+odd));
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y = y+c;
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if nargout > 1
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dy = dy + dc;
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end
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end
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if odd
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if nargout > 1
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dy = y + dy*rho;
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end
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y = y*rho;
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end
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y = prod([1:2:s1])*prod([1:2:s2])*y;
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if nargout > 1
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dy = prod([1:2:s1])*prod([1:2:s2])*dy;
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end
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