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Topic: Bootstrap: Skewness and Kurtosis, normal data
Replies: 0

 Luis A. Afonso Posts: 4,758 From: LIsbon (Portugal) Registered: 2/16/05
Bootstrap: Skewness and Kurtosis, normal data
Posted: Nov 20, 2013 5:22 PM

Bootstrap: Skewness and Kurtosis, normal data

A rather futile exercise, again. . .

__2__It is able to reconstruct the Population.
__3__In the Population each sample item have the same probability to occur, therefore we can safely to sample from the Source with replacement with probability 1/n.
__4__Repeated values (continuous Distribution) are as likewise than different ones.
__5__The set of real samples could be perfectly represented with the n items the Source have.
_____________

The Exercise:

One normal (standard) item X( ) is simulated through the Box-Muller model. Repeating m=2000 times the Source is built and the Skewness and Kurtosis, |S0|, K0.
The Source is bootstrapped, |S| and K evaluated.

Results:
______ p(|S0| > |S|) = 0.281 to 0.296
_______Z = -21.9 to -20.0
______ p(K0 > K) = 0.562 to 0.584
_______Z = 5.6 to 7.6

Z tests both very significant: the Bootstrap data is not conformable with source ones.
As expected . . .

Luis A. Afonso