In probability and statistics, a random variate is a specific outcome or realization of a random variable, with different values often called random numbers. A random deviate is the difference between a variate and the distribution’s central location, such as the mean, often scaled by the standard deviation as a standard score. Random variates are essential for simulating stochastic processes, typically generated from a uniform distribution of pseudorandom numbers using methods of (uniform) random number generation or non-uniform pseudo-random variate generation. In probability theory, random variates represent values of measurable functions from a probability space to a measurable space.
Definition
Devroye2 defines a random variate generation algorithm (for real numbers) as follows:
Assume that- Computers can manipulate real numbers.
- Computers have access to a source of random variates that are uniformly distributed on the closed interval [0,1].
(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.)
The distinction between random variable and random variate is subtle and is not always made in the literature. It is useful when one wants to distinguish between a random variable itself with an associated probability distribution on the one hand, and random draws from that probability distribution on the other, in particular when those draws are ultimately derived by floating-point arithmetic from a pseudo-random sequence.
Practical aspects
For the generation of uniform random variates, see Random number generation.
For the generation of non-uniform random variates, see Pseudo-random number sampling.
See also
References
"Deviate: the value of a random variable measured from some standard point of location, usually the mean. It is often understood that the value is expressed in standard measure, i.e., as a proportion of the parent standard deviation." Y. Dodge (Ed.) The Oxford Dictionary of Statistical Terms, [1] https://books.google.com/books?id=_OnjBgpuhWcC&q=deviate&pg=PA112 ↩
Luc Devroye (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag, pp. 1–2. ("Non-Uniform Random Variate Generation". Archived from the original on 2009-05-05. Retrieved 2009-05-05.) /wiki/Luc_Devroye ↩