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# Developments in pseudo‐random number generators

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Monte Carlo simulations have become a common practice to evaluate a proposed statistical procedure, particularly when it is analytically intractable. Validity of any simulation study relies heavily on the goodness of random variate generators for some specified distributions, which in turn is based on the successful generation of independent variates from the uniform distribution. However, a typical computer‐generated pseudo‐random number generator (PRNG) is a deterministic algorithm and we know that no PRNG is capable of generating a truly random uniform sequence. Since the foundation of a simulation study is built on the PRNG used, it is extremely important to design a good PRNG. We review some recent developments on PRNGs with nice properties such as high‐dimensional equi‐distribution, efficiency, long period length, portability, and efficient parallel implementations. WIREs Comput Stat 2017, 9:e1404. doi: 10.1002/wics.1404

Plots of probability density functions. Panel (a) is for X (red), 2X (green), and 5X (blue) with X ∼ Gamma(2, 1) and panel (b) is for Y = cX mod 1, c = 1, 2,5.
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Scatter plots of correlation between pairs of five processors. Panel (a) is for the fixed block method and panel (b) is for the systematic leap frog method.
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Plots of probability density functions for a bivariate normal vector with ρ = 0.99, (X, Y). Panel (a) is for (4X, 4Y) mod 1 and panel (b) is for (8X, 8Y) mod 1.
[ Normal View | Magnified View ]
Plots of probability density functions for a bivariate normal vector with ρ = 0.99, (X, Y). Panel (a) is for (X, Y) mod 1 and panel (b) is for (2X, 2Y) mod 1.
[ Normal View | Magnified View ]

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