Testing Random- Number Generators
Testing RandomNumber Generators
Raj Jain Washington University Saint Louis, MO 63130
Jain@cse.wustl.edu
Audio/Video recordings of this lecture are available at:
Washington University in St. Louis
CSE574s
27-1
?2008 Raj Jain
Overview
1. Chi-square test 2. Kolmogorov-Smirnov Test 3. Serial-correlation Test 4. Two-level tests 5. K-dimensional uniformity or k-distributivity 6. Serial Test 7. Spectral Test
Washington University in St. Louis
CSE574s
27-2
?2008 Raj Jain
Testing Random-Number Generators
Goal: To ensure that the random number generator produces a random stream. ! Plot histograms ! Plot quantile-quantile plot ! Use other tests ! Passing a test is necessary but not sufficient ! Pass Good
Fail Bad ! New tests Old generators fail the test ! Tests can be adapted for other distributions
Washington University in St. Louis
CSE574s
27-3
?2008 Raj Jain
Chi-Square Test
! Most commonly used test ! Can be used for any distribution ! Prepare a histogram of the observed data ! Compare observed frequencies with theoretical k = Number of cells oi = Observed frequency for ith cell ei = Expected frequency
! D=0 Exact fit ! D has a chi-square distribution with k-1 degrees of freedom. Compare D with 2[1-; k-1] Pass with confidence if D is less
Washington University in St. Louis
CSE574s
27-4
?2008 Raj Jain
Example 27.1
! 1000 random numbers with x0 = 1
!
! Observed difference = 10.380
! Observed is Less Accept IID U(0, 1)
Washington University in St. Louis
CSE574s
27-5
?2008 Raj Jain
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