Standard normal deviate

A standard normal deviate (or standard normal variable) is a normally distributed random variable with expected value 0 and variance 1. A fuller term is standard normal random variable. Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections are statistically independent.

Standard normal variables play a major role in theoretical statistics in the description of many types of model, particularly in regression analysis, the analysis of variance and time series analysis.

When the term "deviate" is used, rather than "variable", there is a connotation that the value concerned is treated as the no-longer-random outcome of a standard norm random variable. The terminology here is the same as that for random variable and random variate. Standard normal deviates arise in practical statistics in two ways.

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