Statistical parameter: Difference between revisions

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{{Short description|Quantity that indexes a parametrized family of probability distributions}}

{{Other uses|Parameter (disambiguation)}}

{{redirect|True value|the company|True Value|the logical value|Truth value}}In [[statistics]], as opposed to its general [[parameter|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarisessummarizes or describes an aspect of the population, such as a [[mean]] or a [[standard deviation]]. If a population exactly follows a known and defined distribution, for example the [[normal distribution]], then a small set of parameters can be measured which completelyprovide describesa comprehensive description of the population, and can be considered to define a [[probability distribution]] for the purposes of extracting [[Sample (statistics)|sample]]s from this population.

{{redirect|True value|the company|True Value|the logical value|Truth value}}

[[File:World population distribution.svg|thumb|World population distribution]]

A "parameter" is to a [[statistical population|population]] as a "[[statistic]]" is to a [[statistical sample|sample]]; that is to say, a parameter describes the '''true value''' calculated from the full population (such as the [[population mean]]), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the [[sample mean]], which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a '''population parameter'''.<ref name="ESS06">{{citation| title= Parameter | encyclopedia= [[Encyclopedia of Statistical Sciences]] | editor1-first= S. | editor1-last= Kotz | editor1-link= Samuel Kotz |display-editors=etal | year= 2006 | publisher= [[Wiley (publisher)|Wiley]]}}.</ref><ref>Everitt, B. S.; Skrondal, A. (2010), ''The Cambridge Dictionary of Statistics'', [[Cambridge University Press]].</ref>

In [[statistics]], as opposed to its general [[parameter|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarises or describes an aspect of the population, such as a [[mean]] or a [[standard deviation]]. If a population exactly follows a known and defined distribution, for example the [[normal distribution]], then a small set of parameters can be measured which completely describes the population, and can be considered to define a [[probability distribution]] for the purposes of extracting [[Sample (statistics)|sample]]s from this population.

A parameter is to a [[statistical population|population]] as a [[statistic]] is to a [[statistical sample|sample]]; that is to say, a parameter describes the '''true value''' calculated from the full population, whereas a statistic is an estimated measurement of the parameter based on a sample. Thus a "statistical parameter" can be more specifically referred to as a '''population parameter'''.<ref name="ESS06">{{citation| title= Parameter | encyclopedia= [[Encyclopedia of Statistical Sciences]] | editor1-first= S. | editor1-last= Kotz | editor1-link= Samuel Kotz |display-editors=etal | year= 2006 | publisher= [[Wiley (publisher)|Wiley]]}}.</ref><ref>Everitt, B. S.; Skrondal, A. (2010), ''The Cambridge Dictionary of Statistics'', [[Cambridge University Press]].</ref>

==Discussion==