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Diffstat (limited to 'report/figures/tracy-widom-approx/tracywidom_appx.m')
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diff --git a/report/figures/tracy-widom-approx/tracywidom_appx.m b/report/figures/tracy-widom-approx/tracywidom_appx.m new file mode 100644 index 0000000..bbab815 --- /dev/null +++ b/report/figures/tracy-widom-approx/tracywidom_appx.m @@ -0,0 +1,38 @@ +function [pdftwappx, cdftwappx] = tracywidom_appx(x, i) +% +% +% [pdftwappx, cdftwappx]=tracywidom_appx(x, i) +% +% SHIFTED GAMMA APPROXIMATION FOR THE TRACY-WIDOM LAWS, by M. Chiani, 2012 +% +% TW ~ Gamma[k,theta]-alpha +% +% [pdf,cdf]=tracywidom_appx(x,2) gives the approximated pdf(x) and CDF(x) of the TW2 +% +% [pdf,cdf]=tracywidom_appx(x,i) for i=1,2,4 gives TW1, TW2, TW4 +% +% see paper M.Chiani, "Distribution of the largest eigenvalue for real +% Wishart and Gaussian random matrices and a simple approximation for the +% Tracy-Widom distribution", submitted 2012, ArXiv +% +kappx = [46.44604884387787, 79.6594870666346, 0, 146.0206131050228]; % K, THETA, ALPHA +thetaappx = [0.18605402228279347, 0.10103655775856243, 0, 0.05954454047933292]; +alphaappx = [9.848007781128567, 9.819607173436484, 0, 11.00161520109004]; +cdftwappx = cdfgamma(x+alphaappx(i), thetaappx(i), kappx(i)); % Chiani's appx: Tracy-Widom as a shifted Gamma +pdftwappx = pdfgamma(x+alphaappx(i), thetaappx(i), kappx(i)); % Chiani's appx: Tracy-Widom as a shifted Gamma +end +function [pdfgamma]=pdfgamma(x, ta, ka) % Utility: PDF of a Gamma + if(x > 0) + pdfgamma=1/(gamma(ka)*ta^ka) * x.^(ka - 1) .* exp(-x/ta); + else + pdfgamma=0 ; + end +end +function[cdfgamma]=cdfgamma(x, ta, ka) % Utility: CDF of a Gamma + if(x > 0) + cdfgamma=gammainc(x/ta,ka); + else + cdfgamma=0; + end + +end |