Random-Number Generation
Random-Number
Generation
?2010 Raj Jain
26-1
Overview
Desired properties of a good generator
? Linear-congruential generators
? Tausworthe generators
? Survey of random number generators
? Seed selection
? Myths about random number generation
?
?2010 Raj Jain
26-2
Random-Number Generation
Random Number = Uniform (0, 1)
? Random Variate = Other distributions
= Function(Random number)
?
?2010 Raj Jain
26-3
A Sample Generator
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For example,
?
Starting with x0=5:
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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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?2010 Raj Jain
26-4
Terminology
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?
?
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Seed = x0
Pseudo-Random: Deterministic yet would pass randomness
tests
Fully Random: Not repeatable
Cycle length, Tail, Period
?2010 Raj Jain
26-5
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