Variate

A variate is a generalization of the concept of a random variable that is defined without reference to a particular type of probabilistic experiment. It is defined as the set of all random variables that obey a given probabilistic law.

It is common practice to denote a variate with a capital letter (most commonly ). The set of all values that  can take is then called the range, denoted  (Evans et al. 2000, p. 5). Specific elements in the range of  are called quantiles and denoted , and the probability that a variate  assumes the value  is denoted .

REFERENCES:

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, 2000.

Kenney, J. F. and Keeping, E. S. "Variates." §1.2 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 5-6, 1962.