Interpreting the test result on a RNG
- From: "Cristiano" <cristiano.pi@xxxxxxxxxx>
- Date: Mon, 12 Feb 2007 13:21:25 +0100
On page 100 (page 109 of the pdf file) of this NIST paper
http://csrc.nist.gov/publications/nistpubs/800-22/sp-800-22-051501.pdf
there is an interpretation method of the result obtained from a test of a
random number generator.
The range of acceptable proportion of sequences that pass the test is
determined using the confidence interval calculated using a normal
distribution as an approximation to the binomial distribution.
I'd like to implement that method using the binomial distribution because
the number of the tested sequences ('m' in the paper) can be 50 or 100.
I calculated the following table with m=50 and a=0.05:
F Bin CUM(Bin)
0 0.076945 0.923055
1 0.202487 0.720568
2 0.261101 0.459467
3 0.219875 0.239592
4 0.135975 0.103617
5 0.065841 0.037776
6 0.025990 0.011786
7 0.008598 0.003188
F is the number of the sequences which failed the test (p-value < a)
Bin is Pp(n|N) in this link (the binomial distribution):
http://mathworld.wolfram.com/BinomialDistribution.html
CUM(bin) is the probability to see more than F failures.
My problem is: which column should I use? Or, in other words, the overall
test is one-tailed (column 'CUM(Bin)') or two-tailed (column 'Bin')? I think
the latter.
Thanks
Cristiano
.
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