Random variate

In the mathematical fields of probability and statistics, a random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable might have different values. Random variates are used when simulating processes driven by random influences (). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers.

Procedures to generate random variates corresponding to a given distribution are known as procedures for random variate generation or pseudo-random number sampling.

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. In that context, and in statistics, those values are known as a random variates, or occasionally random deviates, and this represents a wider meaning than just that associated with pseudorandom numbers.

Devroye defines a random variate generation algorithm (for real numbers) as follows:

(Both assumptions are violated in most real computers. Computers necessarily lack the ability to manipulate real numbers, typically using floating point representations instead. Most computers lack a source of true randomness (like certain hardware random number generators), and instead use pseudorandom number sequences.)

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