Developer Reference

Contents

Chi-Squared Goodness-of-Fit Test

Test Purpose
The test verifies that the sample distribution function agrees with the hypothesized distribution. A chi-squared
V
statistic with the number of degrees of freedom that is minus one from the number of the intervals of partition is considered a stable response.
First Level Test
For a given parameter set and a given sample size, the test computes the partition of the distribution domain into disjoint intervals, so that the a priori quantity of random numbers from each interval is of order 100.
The test computes the actual number of random values within each interval of the generated sample and then calculates chi-square of the statistic
V
. The statistic
V
is asymptotically of chi-squared distribution
Fk-1(x)
with
k
- 1 degrees of freedom, where
k
is the number of the intervals. Thus, the p-value equal to
Fk-1(V)
should be of a distribution that is close to uniform.
Second Level Test
The first level test is run ten times, each run producing a p-value
pj
,
j
= 1, 2, ... , 10. The Kolmogorov-Smirnov goodness-of-fit test with Anderson-Darling’s statistics is applied to the obtained p-values
pj
j
= 1, 2, ... , 10. If the resulting p-value
pM
Interpreting Final Results
The final result of the test is the percentage FAIL of failed second level tests. The second level test is run ten times. The value of FAIL < 50% is considered acceptable.

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804