This section describes VSL Continuous Distribution Functions:
Random number generator of the gamma distribution with parameters shape α, offset a, and scale factor β. You can generate any successive random number γα of the standard gamma distribution (a = 0, β = 1) as follows:
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VSL provides an option of producing an exact copy of a generated stream by calling the vslCopyStream function:
Most of empirical tests used for the VSL BRNGs are well documented (for example, see [Mars95], [Ziff98]). This section describes these tests and the testing procedure in greater detail since tests may vary in their applicability and implementation for a particular BRNG. In addition, this section provides figures of merit that are used to decide on passing vs.
This is a 32-bit combined multiple recursive generator with two components of order 3:
MRG32k3a combined generator meets the requirements for modern RNGs, such as good multidimensional uniformity, or a long period. Optimization for various Intel® architectures makes it competitive with the other VSL BRNGSs in terms of speed.
Random number generator of uniform distribution over the real interval [a,b). You may identify the underlying BRNG by passing the random stream descriptor stream as a parameter. Then the Uniform function calls real implementation (of single precision for vsRngUniform and of double precision for vdRngUniform) of this BRNG.
Random number generator of the beta distribution with two shape parameters p and q, offset a, and scale factor β. You can generate any successive random number Θ(p,q) of the standard gamma distribution (a = 0, β = 1) as follows:
Computer simulation has become a new and commonly recognized approach to scientific research along with conventional experimentation. The latter harshly restricts a mathematical model that is supposed to be as sophisticated as the available conventional research methods permit. As for computer simulation, with ever-growing computing power, the degree of mathematical model complexity depends mainly on the researchers' understanding of phenomena they try to model.
Typically, to get one more correct decimal digit in Monte Carlo, you need to increase the sample by the factor of 100. That makes Monte Carlo applications computationally expensive. Some of them take days or weeks while others may take several months of computations. For such applications, saving intermediate results to a file is essential to be able to continue computation using that result in case the application is terminated intentionally or abnormally.