# Solved – Bootstrapping and Kolmogorov-Smirnov

Here is an experiment I did:

1. I bootstrapped a sample \$S\$ and stored the results as empirical distribution under the name \$S_1\$.
2. Then I bootstrapped \$i=10000\$ times in a row the same sample \$S\$ and compare the resulting empirical distributions \$S_i\$ with \$S_1\$ using Kolmogorov-Smirnov test .

Results from the experiment: The comparisons return different \$p\$-values (from \$0.01\$ to \$0.99\$) and different \$D\$ values (from \$0.02\$ to \$0.06\$).

Is that expected? If I bootstrap the same sample 1000 times isn't it expected that all 1000 empirical distributions to be from the same distribution?

If yes then should I try to establish the distribution of the empirical distributions (\$S_1\$, \$S_i\$)?

For instance:
Three empirical distributions \$S_1\$, \$S_2\$, \$S_3\$ bootstrapped from the same initial sample \$S\$:

``S1: 1,2,3,4,5,6 S2: 1,3,4,5,6,7 S3: 2,4,5,6,7,8 ``

If I add them up I get:

``1,1,2,2,3,3,4,4,4,5,5,5,6,6,6,7,7,8 ``
Contents