CPE 619 Testing Random-Number Generators. Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in Huntsville http://www.ece.uah.edu/~milenka http://www.ece.uah.edu/~lacasa. Overview. Chi-square test Kolmogorov-Smirnov Test
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The LaCASA Laboratory
Electrical and Computer Engineering Department
The University of Alabama in Huntsville
Goal: To ensure that the random number generator produces a
Þ Compare D with c2[1-a; k-1] Pass with confidence a if D is less
For k1 Check if CI includes zero
10,000 random numbers with x0=1:
Þ Use Chi-square test on n samples of size k each and then use a Chi-square test on the set of n Chi-square statistics so obtained
Þ Chi-square on Chi-square test.
For all choices of a1, b1, a2, b2 in [0, 1], b1>a1 and b2>a2
All points lie on three straight lines.
Or:Example 27.6: Spectral Test
Obtained by adding the following to equation
Note that k+k1 will be an integer between 0 and 4.
Þ Both sequences will pass the chi-square test for uniformity
See Knuth (1981)
Is CDF a sum
of other CDFs?
Is pdf a sum
of other pdfs?
variate a sum of other
variate related to other
a majorizing function
Use empirical inversion