File:Medcouple-distribution.png
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Summary
| Description |
English: Histogram of 5000 random values taken from a gamma distribution with parameters alpha = 3 and beta = 2, with corresponding histogram of the 6.25 million values of the medcouple kernel. The actual medcouple, the median of the second histogram, is at 0.188994, marked with a yellow line.
This was produced by the following GNU Octave code. # Set the seed, to make this "random" sampling deterministic
randg("seed", 0);
z = gamrnd (3, 2, 5e3, 1);
# Plot the gamma values
subplot(2,1,1);
hist(z,20, "facecolor", [1, 0.5, 0.5]);
title("gamma distribution with alpha=3 and beta=2", "fontsize", 20);
set(gca, "fontsize", 14)
# Naive medcouple algorithm
n = length(z);
n2 = ceil(n/2);
z = sort(z, "descend");
zmed = median(z);
z -= zmed;
zplus = z(z >= 0);
zminus = z(z <= 0)';
zz = (zplus + zminus)./(zplus - zminus);
zz(isnan(zz)) = 0;
zzsort = sort(zz(:), "descend");
medc_idx = ceil(n2^2/2);
mc = zzsort(medc_idx);
# Plot the medcouple distribution
subplot(2,1,2);
hist(zzsort,20, "facecolor", [0.5, 0.5, 1]);
# Draw the medcouple line on the medcouple distribution
hold on;
plot([mc,mc], [0,5e5], "linewidth", 2.5, "color", [0.95, 0.95, 0]);
title("distribution of h(x_i, x_j) values", "fontsize", 20);
set(gca,"xtick", [-1, -0.5, mc, 0.5, 1], "fontsize", 14);
hold off
print medcouple-distribution.png
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| Date | |
| Source | Own work |
| Author | Jordi Gutiérrez Hermoso |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:41, 6 April 2015 | | 1,200 × 900 (45 KB) | JordiGH | User created page with UploadWizard |
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