Random Number Generation - Other Considerations

Other Considerations

Random numbers uniformly distributed between 0 and 1 can be used to generate random numbers of any desired distribution by passing them through the inverse cumulative distribution function (CDF) of the desired distribution. Inverse CDFs are also called quantile functions. To generate a pair of statistically independent standard normally distributed random numbers (x, y), one may first generate the polar coordinates (r, θ), where r~χ₂2 and θ~UNIFORM(0,2π) (see Box–Muller transform).

Some 0 to 1 RNGs include 0 but exclude 1, while others include or exclude both.

The outputs of multiple independent RNGs can be combined (for example, using a bit-wise XOR operation) to provide a combined RNG at least as good as the best RNG used. This is referred to as software whitening.

Computational and hardware random number generators are sometimes combined to reflect the benefits of both kinds. Computational random number generators can typically generate pseudo-random numbers much faster than physical generators, while physical generators can generate "true randomness."