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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)));

I tried this code: x = randn(100000,1); L = lmom(x,4) L = 0.0038 0.5650 0.0005 0.0685

In fact L4 != 0.1226 !!!

but you can evaluate: T4 = L4/L2 = 0.1213

ok, I found it

I generated 1000 random nos from normal distribution(5,0.2)..i tried lmom(x)...the first three moments are right but the 4 moment kurtosis comes around 0.0137 while L4 for a normal dist is 0.1226...What is causing this discrepancy?

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