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T4 calculation is correct. Actually the estimate of T4 is random variable by itself, which follows normal distribution asymptotically.

Following code illustrate the idea, and the sample mean T4 approach 0.1226 in the long run.

N = 10000; ks = ones(N,1); for i=1:N x = randn(1000,1); l = lmom(x,4); ks(i) = l(4)/l(2); end hist(ks,100); title(sprintf('Avg.T4=%.4f',mean(ks)));

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