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Examples
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Corner test: realizations in [0, a] 2 a = 0.0005, 104 realizations ©EADS IW 2010 BigMC seminar, January 28th 2010
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Multiplicative congruential generators Demonstration (2/3) 1 If α0 + · · · + αd − 1 ad − 1 ≡ 0 mod m, σ = α0 un +
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Fast and high-quality normal PRNG The ziggurat method (Marsaglia) How to use it?
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Corner test: realizations in [0, a] 2 a = 0.05, 104 realizations ©EADS IW 2010 BigMC seminar, January 28th 2010
Recently Uploaded Slideshows regislebrun 2010
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Pseudo-random numbers generator (PRNG) Any one who considers arithmetical methods of producing random digits is, of coures, in a state of sin.
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Statistical tests The spectral test Compute the normalized quantity: π d/2 νd d µd = (5) Γ (d/2 + 1) m The test is successful if µd >
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs Fast and high-quality normal PRNG The ziggurat method (Marsaglia) √ 2π The acceptation ratio is ρ = 2NV, so we use large values for N, such as N = 128, for which ρ 98. 78%.
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Pseudo-random number generator Discretization scheme 4
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs What is a pseudo-number generator?
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Pseudo-random number generators Uniform PRNGs Non-uniform PRNGs LCGs and the ratio of uniforms method Gap for usual distributions We consider the Cauchy, normal and exponential distributions for LCGs with m 232 and q2 varying from 0.1 to 1.
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