The diehard tests are a battery of statistical tests for measuring the quality of a set of random numbers. A statistical hypothesis test is a method of making statistical decisions using experimental data Random number may refer to A number generated for or part of a set exhibiting Statistical randomness. They were developed by George Marsaglia over several years and first published in 1995 on a CD-ROM of random numbers. George Marsaglia is a mathematician and computer scientist He is perhaps best known for establishing the lattice structure of congruential random number generators in the paper "Random CD-ROM (an initialism of "Compact Disc Read-Only Memory " is a pre-pressed Compact Disc that contains data accessible to but not writable

The tests are:

• Birthday spacings: Choose random points on a large interval. The spacings between the points should be asymptotically Poisson distributed. In Probability theory and Statistics, the Poisson distribution is a Discrete probability distribution that expresses the probability of a number of events The name is based on the birthday paradox. In Probability theory, the birthday problem, pertains to the Probability that in a set of Randomly chosen people some pair of them will have the same

• 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. The column rank of a matrix A is the maximal number of Linearly independent columns of A. 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 don't appear should follow a known distribution. The name is based on the infinite monkey theorem. The infinite monkey theorem states that a Monkey hitting keys at Random on a Typewriter keyboard for an Infinite amount of time will almost

• 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. The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields

• 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. WikipediaWikiProject Probability#Standards for a discussionof standards used for probability distribution articles such as this one

• 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). The runs test (also called Wald - Wolfowitz test) is a non-parametric test that checks a randomness hypothesis for a two-valued data sequence 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. Craps is a Dice game played against other players or a bank Craps developed from a simplification of the Old English game hazard. Each count should follow a certain distribution.

See also

• Randomness test

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

Randomness tests (or tests of randomness) in data evaluation are used to analyze the distribution pattern of a set of data

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