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If a given sequence was able to pass all of these tests within a given degree of significance (generally 5%), then it was judged to be, in their words "locally random". Kendall and Smith differentiated "local randomness" from "true randomness" in that many sequences generated with truly random
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produced by "truly random" processes, but rather by deterministic algorithms. Over the history of random number generation, many sources of numbers thought to appear "random" under testing have later been discovered to be very non-random when subjected to certain types of tests. The notion of
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randomness refers to the idea that there can be minimum sequence lengths in which random distributions are approximated. Long stretches of the same numbers, even those generated by "truly" random processes, would diminish the "local randomness" of a sample (it might only be locally random for
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large sequences might contain many rows of a single digit. This might be "random" on the scale of the entire sequence, but in a smaller block it would not be "random" (it would not pass their tests), and would be useless for a number of statistical applications.
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As random number sets became more and more common, more tests, of increasing sophistication were used. Some modern tests plot random digits as points on a three-dimensional plane, which can then be rotated to look for hidden patterns. In 1995, the statistician
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numbers was developed to circumvent some of these problems, though pseudorandom number generators are still extensively used in many applications (even ones known to be extremely "non-random"), as they are "good enough" for most applications.
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test treats each output bit of the random number generator as a coin flip test, and determine if the observed number of heads and tails are close to the expected 50% frequency. The number of heads in a coin flip trail forms a
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look random. In a "truly" random sequence of numbers of sufficient length, for example, it is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random.
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are different. Most philosophical conceptions of randomness are global—because they are based on the idea that "in the long run" a sequence looks truly random, even if certain sub-sequences would
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that were developed to distinguish whether experimental phenomena matched their theoretical probabilities. Pearson developed his test originally by showing that a number of dice experiments by
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the idea that each number in a given random sequence had an equal chance of occurring, and that various other patterns in the data should be also distributed equiprobably.
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showed that NIST SP800-22 testing standards are not sufficient to detect some weakness in randomness generators and proposed statistically distance based randomness test.
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tests for the number of bit transitions between 0 bits, and 1 bits, comparing the observed frequencies with expected frequency of a random bit sequence.
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298:- performing a Fourier transform on a "random" signal transforms it into a sum of periodic functions in order to detect non random repetitive trends
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192:, looked at the distances between zeroes (00 would be a distance of 0, 030 would be a distance of 1, 02250 would be a distance of 3, etc.).
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Wang, Yongge; Nicol, Tony (2015). "Statistical
Properties of Pseudo Random Sequences and Experiments with PHP and Debian OpenSSL".
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sequences of 10,000 numbers; taking sequences of less than 1,000 might not appear random at all, for example).
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A sequence exhibiting a pattern is not thereby proved not statistically random. According to principles of
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Yongge Wang: On the Design of LIL Tests for (Pseudo) Random
Generators and Some Experimental Results.
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distributed a Java software package for statistically distance based randomness testing.
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require tests as exclusive verifications for their "randomness," as they are decidedly
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Testing Techniques For Pseudorandom generation.
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The Art of
Computer Programming Vol. 2 : Seminumerical Algorithms
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Quality of a numerical sequence of having no recognizable patterns
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Pi seems a good random number generator – but not always the best
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is sufficient for many uses, such as statistics, hence the name
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might not display "local randomness" to a given degree —
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or regularities; sequences such as the results of an ideal
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Statistical randomness does not necessarily imply "true"
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imposes certain standards of statistical randomness to
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in 1938. They were built on statistical tools such as
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The first tests for random numbers were published by
288:Statistically distance based randomness test.
151:Kendall and Smith's original four tests were
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533:Generating Normal Distributed Random Numbers
438:http://webpages.uncc.edu/yonwang/liltest/
403:Journal of the Royal Statistical Society
137:Journal of the Royal Statistical Society
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214:created a set of tests known as the
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301:Maurer's Universal Statistical Test
148:did not display "random" behavior.
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38:when it contains no recognizable
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99:complete disorder is impossible
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234:Pseudorandom number generators
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323:Complete spatial randomness
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475:10.1016/j.cose.2015.05.005
358:Seven states of randomness
142:Pearson's chi-squared test
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529:Random Number Test Suite.
267:Wald–Wolfowitz runs test
284:Kolmogorov–Smirnov test
132:Bernard Babington Smith
104:Legislation concerning
548:Statistical randomness
488:Knuth, Donald (1998).
463:Computers and Security
318:Algorithmic randomness
155:, which took as their
260:binomial distribution
36:statistically random
18:Statistically random
273:Information entropy
226:numbers. In 2015,
222:of 5 billion
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386:Purdue University
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59:unpredictability
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521:: A free (
369:References
343:Randomness
179:poker test
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30:A numeric
519:DieHarder
469:: 44–64.
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312:See also
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363:TestU01
255:Monobit
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