Random variate

In <a href="/facts/Probability/fgYvMhwb">probability</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a random variate or simply variate is a particular outcome or <a href="/facts/Realization_(probability)/lDklUzqX">realization</a> of a <a href="/facts/Random_variable/TwTBXnLT">random variable</a>; the random variates which are other outcomes of the same random variable might have different values (<a href="/facts/Random_number/lSGGA5gW">random numbers</a>).
A random deviate or simply deviate is the difference of a random variate with respect to the distribution <a href="/facts/Central_location_(statistics)/9yhcQ6me">central location</a> (e.g., <a href="/facts/Mean/swcEd4Pg">mean</a>), often divided by the <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a> of the distribution (i.e., as a <a href="/facts/Standard_score/lF8v0Mcy">standard score</a>).
Random variates are used when <a href="/facts/Simulation/Q4QJV1oI">simulating</a> processes driven by random influences (<a href="/facts/Stochastic_processes/Ng1n1dnB">stochastic processes</a>). In modern applications, such simulations would derive random variates corresponding to any given <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> from computer procedures designed to create random variates corresponding to a <a href="/facts/Uniform_distribution_(continuous)/XbnlVljT">uniform distribution</a>, where these procedures would actually provide values chosen from a <a href="/facts/Uniform_distribution_(continuous)/XbnlVljT">uniform distribution</a> of <a href="/facts/Pseudorandom/kfs1wfhY">pseudorandom</a> numbers.
Procedures to generate random variates corresponding to a given distribution are known as procedures for (uniform) <a href="/facts/Random_number_generation/RtXEfbzd">random number generation</a> or <a href="/facts/Non-uniform_pseudo-random_variate_generation/xIkyQJqu">non-uniform pseudo-random variate generation</a>.
In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, a random variable is a <a href="/facts/Measurable_function/NgIHnb1b">measurable function</a> from a <a href="/facts/Probability_space/dEcv2VrU">probability space</a> to a <a href="/facts/Measurable_space/AJ98lhT4">measurable space</a> of values that the variable can take on. In that context, those values are also known as random variates or random deviates, and this represents a wider meaning than just that associated with <a href="/facts/Pseudorandom/kfs1wfhY">pseudorandom</a> numbers.

Random variate open-in-new

Random variate