Random-Number Generation
[Pages:46]Random-Number Generation
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?2010 Raj Jain
Overview
Desired properties of a good generator Linear-congruential generators Tausworthe generators Survey of random number generators Seed selection Myths about random number generation
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Random-Number Generation
Random Number = Uniform (0, 1) Random Variate = Other distributions
= Function(Random number)
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?2010 Raj Jain
A Sample Generator
For example,
Starting with x0=5:
The first 32 numbers obtained by the above procedure 10, 3, 0, 1, 6, 15, 12, 13, 2, 11, 8, 9, 14, 7, 4, 5 10, 3, 0, 1, 6, 15, 12, 13, 2, 11, 8, 9, 14, 7, 4, 5.
By dividing x's by 16: 0.6250, 0.1875, 0.0000, 0.0625, 0.3750, 0.9375, 0.7500, 0.8125, 0.1250, 0.6875, 0.5000, 0.5625, 0.8750, 0.4375, 0.2500, 0.3125, 0.6250, 0.1875, 0.0000, 0.0625, 0.3750, 0.9375, 0.7500, 0.8125, 0.1250, 0.6875, 0.5000, 0.5625, 0.8750, 0.4375, 0.2500, 0.3125.
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Terminology
Seed = x0 Pseudo-Random: Deterministic yet would pass randomness
tests Fully Random: Not repeatable Cycle length, Tail, Period
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Desired Properties of a Good Generator
It should be efficiently computable. The period should be large. The successive values should be independent and
uniformly distributed
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Types of Random-number Generators
Linear congruential generators Tausworthe generators Extended Fibonacci generators Combined generators
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Linear-Congruential Generators
Discovered by D. H. Lehmer in 1951 The residues of successive powers of a number have good
randomness properties.
Equivalently,
a = multiplier m = modulus
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?2010 Raj Jain
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