Diehard tests

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 exponentially distributed.^[1] The name is based on the 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 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 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. If the circle overlaps an existing one, try again. After 12,000 tries, the number of successfully "parked" circles should follow a certain 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 2³¹ by random floats on (0,1) 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 (0,1). Add sequences of 100 consecutive floats. The sums should be normally distributed with characteristic mean and sigma.

• Runs test: Generate a long sequence of random floats on (0,1). Count ascending and descending runs. The counts should follow a certain distribution.

• The craps test: Play 200,000 games of craps, counting the wins and the number of throws per game. Each count should follow a certain distribution.

See also

• Randomness test
• TestU01

Notes

External links

• The Marsaglia Random Number CDROM including the Diehard Battery of Tests of Randomness
• Mirror site
• 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 Akadémiai Kiadó