163.118.206.153 at 20:13, 13 February 2025

2025-02-13T20:13:41Z

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{{short description|Normally distributed deviate}}
A '''standard normal deviate''' is a [[normal distribution|normally distributed]] [[deviate (statistics)|deviate]]. It is a [[realization (statistics)|realization]] of a '''standard normal random variable''', defined as a [[random variable]] with [[expected value]] 0 and [[variance]] 1.<ref>Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms. OUP. {{isbn|0-19-920613-9}}</ref> 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 models, 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 normal 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.
*Given a model for a set of observed data, a set of manipulations of the data can result in a derived quantity which, assuming that the model is a true representation of reality, is a standard normal deviate (perhaps in an approximate sense). This enables a [[significance test]] to be made for the validity of the model.
*In the computer generation of a [[pseudorandom number sequence]], the aim may be to generate random numbers having a [[normal distribution]]: these can be obtained from standard normal deviates (themselves the output of a pseudorandom number sequence) by multiplying by the scale parameter and adding the location parameter. More generally, the generation of pseudorandom number sequence having other [[marginal distribution]]s may involve manipulating sequences of standard normal deviates: an example here is the [[chi-squared distribution]], random values of which can be obtained by adding the squares of standard normal deviates (although this would seldom be the fastest method of generating such values).

==See also==
*[[Standard normal table]]

==References==
<references/>

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[[Category:Normal distribution]]

Standard normal deviate - Revision history

163.118.206.153 at 20:13, 13 February 2025