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Distribution Moments Test

Test Purpose
The test verifies that sample moments of a given distribution agree with theoretical moments. Sample mean (first order moment) and sample variance (central moment of the second order) are considered as stable responses.
First Level Test
The generated random number sequence is used to compute the sample mean
M
and the sample variance
D
that are of an asymptotically normal distribution. Proceeding from this asymptotic, p-values
pM
and
pD
are found using the values of
M
and
D
.
Second Level Test
The first level test is run ten times, each run producing a pair of p-values
pM
and
pD
,
j
= 1, 2, ... , 10. The Kolmogorov-Smirnov goodness-of-fit test with Anderson-Darling’s statistics is applied to the obtained p-values
pjM
,
j
= 1, 2, ... , 10. If the resulting p-value
pM
< 0.05 or
pM
> 0.95, the test is considered failed for the sample mean. The same procedure is performed for p-values
pjD
,
j
= 1, 2, ... , 10, and if p-value
pD
< 0.05 or
pD
> 0.95, the test is considered failed for the sample variance.
Interpreting Final Results
Ten runs of the second level test provide the percentage FAILM of failed tests for the sample mean and the percentage FAILD of failed tests for the sample variance. The final result of the test is the percentage FAIL = max(FAILM, FAILD ). The value of FAIL < 50% is considered acceptable.

Product and Performance Information

1

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Notice revision #20110804