# Variate / Random Variate

Contents:

1. Variate
2. Random Variate

## 1. What is a Variate?

The word “variate” means something slightly different, depending on where you’re reading about it. It’s a very loosely defined word, which is one reason why the term isn’t used much in statistics.

1. The Wolfram definition states it is a generalized random variable; one that isn’t attached to a particular probabilistic experiment. This theoretical set is contained within a range and is usually denoted with a capital letter (e.g. X or Y).
2. Dictionary.com defines it simply as “random variable“— without any qualifiers as in the Wolfram definition. The OECD Glossary of Statistical Terms and several authors (including Valkenburg, 2002) also agree with this particular definition.
3. Some authors (e.g. Hájek, 2001) use the word variate as another name for variable. Wiktionary.org seems to agree with this definition, stating that it is “A measurable quantity capable of taking on a number of values.”

Most statistical texts seem to agree with definition #1, even if they don’t explicitly say so. Definition #2 is also common. As far as statistics in general is concerned (i.e. looking at the big picture), the terms univariate analysis and multivariate analysis refer to one-variable and multi-variable analysis, so that’s really on par with definition 3 (although one could argue that these deal with the types of random variables seen in definition 1). Your best bet: check with your particular text to see if you can glean information about the author’s intent. And remember that the definition has many different definitions, so try not to get caught up on which one is precisely right.

## 2. Random Variates

Unlike the term “variate”, there is a consensus for defining a random variate: it’s the random numbers generated from a particular probability distribution. For example, “Pareto variates” are numbers generated from a Pareto distribution.

## References

Hájek, P. (2001). Metamathematics of Fuzzy Logic. Springer Science and Business Media.