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Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator .
Procedures to generate random variates corresponding to a given distribution are known as procedures for (uniform) random number generation or non-uniform pseudo-random variate generation. In probability theory, a random variable is a measurable function from a probability space to a measurable space of values that the variable can take on.
Pages in category "Non-uniform random numbers" ... Non-uniform random variate generation; R. Ratio of uniforms; Rejection sampling; S. Slice sampling; Z. Ziggurat ...
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function.
However, generally they are considerably slower (typically by a factor 2–10) than fast, non-cryptographic random number generators. These include: Stream ciphers. Popular choices are Salsa20 or ChaCha (often with the number of rounds reduced to 8 for speed), ISAAC, HC-128 and RC4. Block ciphers in counter mode.
The particular advantage of this type of approach is that it allows advantage to be taken of existing software for generating random variates from other, usually non-uniform, distributions. However, faster algorithms may be obtainable for the same distributions by other more complicated approaches.
On the other hand, the uniformly distributed numbers are often used as the basis for non-uniform random variate generation. If u {\displaystyle u} is a value sampled from the standard uniform distribution, then the value a + ( b − a ) u {\displaystyle a+(b-a)u} follows the uniform distribution parameterized by a {\displaystyle a} and b ...
Random variate generation Further information: Non-uniform random variate generation A conceptually very simple method for generating exponential variates is based on inverse transform sampling : Given a random variate U drawn from the uniform distribution on the unit interval (0, 1) , the variate