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The '''diehard tests''' are a battery of statistical tests for measuring the quality of a random number generator. They were developed by George Marsaglia over several years and first published in 1995 on a CD-ROM of random numbers.

These are the tests:

* '''Birthday spacings''': Choose random points on a large interval. The spacings between the points should be asymptotically [[wikipedia:exponential distribution|exponentially distributed]].<ref>Renyi, 1953, p194</ref> The name is based on the [[wikipedia:birthday paradox|birthday paradox]].

* '''Overlapping permutations''': Analyze sequences of five consecutive random numbers. The 120 possible orderings should occur with statistically equal probability.

* '''Ranks of matrices''': Select some number of bits from some number of random numbers to form a matrix over {0,1}, then determine the [[wikipedia:rank (linear algebra)|rank]] of the matrix. Count the ranks.

* '''Monkey tests''': Treat sequences of some number of bits as "words". Count the overlapping words in a stream. The number of "words" that do not appear should follow a known distribution. The name is based on the [[wikipedia:infinite monkey theorem|infinite monkey theorem]].

* '''Count the 1s''': Count the 1 bits in each of either successive or chosen bytes. Convert the counts to "letters", and count the occurrences of five-letter "words".

* '''Parking lot test''': Randomly place unit circles in a 100 x 100 square. A circle is successfully parked, if it does not overlaps an existing successfully parked one. After 12,000 tries, the number of successfully parked circles should follow a certain [[wikipedia:normal distribution|normal distribution]].

* '''Minimum distance test''': Randomly place 8,000 points in a 10,000 x 10,000 square, then find the minimum distance between the pairs. The square of this distance should be exponentially distributed with a certain mean.

* '''Random spheres test''': Randomly choose 4,000 points in a cube of edge 1,000. Center a sphere on each point, whose radius is the minimum distance to another point. The smallest sphere's volume should be exponentially distributed with a certain mean.

* '''The squeeze test''': Multiply 2<sup>31</sup> by random floats on <nowiki>(0,1)</nowiki> until you reach 1. Repeat this 100,000 times. The number of floats needed to reach 1 should follow a certain distribution.

* '''Overlapping sums test''': Generate a long sequence of random floats on <nowiki>(0,1)</nowiki>. Add sequences of 100 consecutive floats. The sums should be normally distributed with characteristic mean and variance.

* '''[[wikipedia:Wald–Wolfowitz runs test|Runs test]]''': Generate a long sequence of random floats on <nowiki>(0,1)</nowiki>. Count ascending and descending runs. The counts should follow a certain distribution.

* '''The craps test''': Play 200,000 games of [[wikipedia:craps|craps]], counting the wins and the number of throws per game. Each count should follow a certain distribution.

== See also ==
* [[wikipedia:Randomness test]]
* [[wikipedia:TestU01]]

== Notes ==
<references/>

== External links ==
* [http://www.stat.fsu.edu/pub/diehard/ The Marsaglia Random Number CDROM including the Diehard Battery of Tests of Randomness]
* [http://www.cs.hku.hk/~diehard/cdrom/ Mirror site]
* [http://www.phy.duke.edu/~rgb/General/dieharder.php DieHarder: a random number test suite including an alternative GPL implementation of Diehard tests in C]
* Renyi, A (1953). ''On the theory of order statistics'', Acta Mathematica Hungarica [http://www.akademiai.com/content/fn66125484nh5376/ Akadémiai Kiadó]

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