Statistical parameter - Revision history

154.159.252.193: Changed "completely describes the population" because "completely" sounds too broad, Comprehesive is closer to sufficient and implies as much information as the statistician wants in the context of the parameters. "Completely" implies everything, which is not accurate. https://pubmed.ncbi.nlm.nih.gov/22630335/

2024-08-18T06:59:29Z

Changed "completely describes the population" because "completely" sounds too broad, Comprehesive is closer to sufficient and implies as much information as the statistician wants in the context of the parameters. "Completely" implies everything, which is not accurate. https://pubmed.ncbi.nlm.nih.gov/22630335/

← Previous revision		Revision as of 06:59, 18 August 2024
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	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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 provide a 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.

	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]]). 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>		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]]). 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>

Blakocha: Restoring one mistakenly deleted word.

2024-06-16T16:03:31Z

Restoring one mistakenly deleted word.

← Previous revision		Revision as of 16:03, 16 June 2024
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	==Discussion==		==Discussion==
	===Parameterised distributions===		===Parameterised distributions===
	Suppose that we have an [[indexed family]] of . If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.		Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.

	===Measurement of parameters===		===Measurement of parameters===

DMH223344: correct definition

2023-12-19T22:41:33Z

correct definition

← Previous revision		Revision as of 22:41, 19 December 2023
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	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any ~~measured~~ quantity of a [[statistical population]] that summarizes 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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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 (such as the [[population mean]]), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the [[sample mean]]). 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>		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]]). 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>

175.32.192.219 at 01:53, 3 December 2023

2023-12-03T01:53:31Z

← Previous revision		Revision as of 01:53, 3 December 2023
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	==Discussion==		==Discussion==
	===Parameterised distributions===		===Parameterised distributions===
	Suppose that we have an [[indexed family]] of ~~distributions~~. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.		Suppose that we have an [[indexed family]] of . If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.

	===Measurement of parameters===		===Measurement of parameters===

Fgnievinski: /* top */

2023-12-02T01:34:28Z

top

← Previous revision		Revision as of 01:34, 2 December 2023
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	In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarizes 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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarizes 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>		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]]). 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==		==Discussion==

70.162.11.189 at 04:11, 19 September 2023

2023-09-19T04:11:13Z

← Previous revision		Revision as of 04:11, 19 September 2023
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	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarizes 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>		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>

Hildeoc: ce

2023-07-11T18:05:56Z

← Previous revision		Revision as of 18:05, 11 July 2023
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	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.		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 ~~subsample~~. 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>		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==		==Discussion==
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	==Examples==		==Examples==
	During an election, there may be specific percentages of voters in a country who would vote for each particular candidate – these percentages would be statistical parameters. It is impractical to ask every voter before an election occurs what their candidate preferences are, so a sample of voters will be polled, and a statistic (also called an [[estimator]]) – that is, the percentage of the ~~subsample~~ of polled voters – will be measured instead. The statistic, along with an estimation of its accuracy (known as its [[sampling error]]), is then used to make inferences about the true statistical parameters (the percentages of all voters).		During an election, there may be specific percentages of voters in a country who would vote for each particular candidate – these percentages would be statistical parameters. It is impractical to ask every voter before an election occurs what their candidate preferences are, so a sample of voters will be polled, and a statistic (also called an [[estimator]]) – that is, the percentage of the sample of polled voters – will be measured instead. The statistic, along with an estimation of its accuracy (known as its [[sampling error]]), is then used to make inferences about the true statistical parameters (the percentages of all voters).

	Similarly, in some forms of testing of manufactured products, rather than destructively testing all products, only a sample of products are tested. Such tests gather statistics supporting an inference that the products meet specifications.		Similarly, in some forms of testing of manufactured products, rather than destructively testing all products, only a sample of products are tested. Such tests gather statistics supporting an inference that the products meet specifications.

Hildeoc: tweaks

2023-06-24T17:32:00Z

tweaks

← Previous revision		Revision as of 17:32, 24 June 2023
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	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.		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 subsample. 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>		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 subsample. 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==		==Discussion==

	===Parameterised distributions===		===Parameterised distributions===
	Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.		Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.

	===Measurement of parameters===		===Measurement of parameters===
	In [[statistical inference]], parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a [[random sample]] of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out (for example, the number of degrees of freedom in a [[Pearson's chi-squared test]]). Even if a family of distributions is not specified, quantities such as the [[mean]] and [[variance]] can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences about such population parameters.		In [[statistical inference]], parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a [[random sample]] of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out (for example, the number of degrees of freedom in a [[Pearson's chi-squared test]]). Even if a family of distributions is not specified, quantities such as the [[mean]] and [[variance]] can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences about such population parameters.

	===Types of parameters===		===Types of parameters===
Line 26:		Line 25:

	==Examples==		==Examples==
		⚫	During an election, there may be specific percentages of voters in a country who would vote for each particular candidate – these percentages would be statistical parameters. It is impractical to ask every voter before an election occurs what their candidate preferences are, so a sample of voters will be polled, and a statistic (also called an [[estimator]]) – that is, the percentage of the subsample of polled voters – will be measured instead. The statistic, along with an estimation of its accuracy (known as its [[sampling error]]), is then used to make inferences about the true statistical parameters (the percentages of all voters).

⚫	During an election, there may be specific percentages of voters in a country who would vote for each particular candidate – these percentages would be statistical parameters. It is impractical to ask every voter before an election occurs what their candidate preferences are, so a sample of voters will be polled, and a statistic (also called an [[estimator]]) – that is, the percentage of the subsample of polled voters – will be measured instead. The statistic, along with an estimation of its accuracy (known as its [[sampling error]]), is then used to make inferences about the true statistical parameters (the percentages of all voters).

	Similarly, in some forms of testing of manufactured products, rather than destructively testing all products, only a sample of products are tested. Such tests gather statistics supporting an inference that the products meet specifications.		Similarly, in some forms of testing of manufactured products, rather than destructively testing all products, only a sample of products are tested. Such tests gather statistics supporting an inference that the products meet specifications.

	==See also==
	*[[Parameter]]

	== References ==		== References ==
	{{Reflist}}		{{Reflist}}

	{{-}}
	{{Statistics\|inference}}		{{Statistics\|inference}}

Bjankuloski06: Decapitalisation

2022-10-13T23:49:37Z

Decapitalisation

← Previous revision		Revision as of 23:49, 13 October 2022
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	==Discussion==		==Discussion==

	===Parameterised ~~Distributions~~===		===Parameterised distributions===
	Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.		Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family\|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family\|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)\|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.

	===Measurement of ~~Parameters~~===		===Measurement of parameters===
	In [[statistical inference]], parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a [[random sample]] of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out (for example, the number of degrees of freedom in a [[Pearson's chi-squared test]]). Even if a family of distributions is not specified, quantities such as the [[mean]] and [[variance]] can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences about such population parameters.		In [[statistical inference]], parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a [[random sample]] of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out (for example, the number of degrees of freedom in a [[Pearson's chi-squared test]]). Even if a family of distributions is not specified, quantities such as the [[mean]] and [[variance]] can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences about such population parameters.

	===Types of ~~Parameters~~===		===Types of parameters===
	Parameters are given names appropriate to their roles, including the following:		Parameters are given names appropriate to their roles, including the following:
	*[[location parameter]]		*[[location parameter]]

Ffffrr: Importing Wikidata short description: "Quantity that indexes a parametrized family of probability distributions" (Shortdesc helper)

2022-05-01T13:31:03Z

Importing Wikidata short description: "Quantity that indexes a parametrized family of probability distributions" (Shortdesc helper)

← Previous revision		Revision as of 13:31, 1 May 2022
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			{{Short description\|Quantity that indexes a parametrized family of probability distributions}}
	{{Other uses\|Parameter (disambiguation)}}		{{Other uses\|Parameter (disambiguation)}}
	{{redirect\|True value\|the company\|True Value\|the logical value\|Truth value}}		{{redirect\|True value\|the company\|True Value\|the logical value\|Truth value}}

← Previous revision		Revision as of 06:59, 18 August 2024
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	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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 provide a 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.

	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]]). 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>		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]]). 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>

← Previous revision		Revision as of 22:41, 19 December 2023
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	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any ~~measured~~ quantity of a [[statistical population]] that summarizes 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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any quantity of a [[statistical population]] that summarizes 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 (such as the [[population mean]]), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the [[sample mean]]). 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>		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]]). 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>

← Previous revision		Revision as of 04:11, 19 September 2023
Line 4:		Line 4:
	[[File:World population distribution.svg\|thumb\|World population distribution]]		[[File:World population distribution.svg\|thumb\|World population distribution]]

	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.		In [[statistics]], as opposed to its general [[parameter\|use in mathematics]], a '''parameter''' is any measured quantity of a [[statistical population]] that summarizes 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>		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>

← Previous revision		Revision as of 13:31, 1 May 2022
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			{{Short description\|Quantity that indexes a parametrized family of probability distributions}}
	{{Other uses\|Parameter (disambiguation)}}		{{Other uses\|Parameter (disambiguation)}}
	{{redirect\|True value\|the company\|True Value\|the logical value\|Truth value}}		{{redirect\|True value\|the company\|True Value\|the logical value\|Truth value}}