About: Q-Gaussian distribution

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The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints. It is one example of a Tsallis distribution. The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon entropy. The normal distribution is recovered as q → 1.

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rdf:type	yago:WikicatContinuousDistributions yago:Abstraction100002137 yago:Arrangement105726596 yago:Cognition100023271 yago:Distribution105729036 yago:PsychologicalFeature100023100 yago:Structure105726345 yago:WikicatProbabilityDistributions yago:WikicatProbabilityDistributionsWithNon-finiteVariance
rdfs:label	Q-ガウス分布 (ja) Q-Gaussian distribution (en)
rdfs:comment	q-ガウス分布（英: q-Gaussian distribution）は、分散一定の条件下でを最大化して得られる確率分布。物理学者のコンスタンティーノ・ツァリスにより導出された。 (ja) The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints. It is one example of a Tsallis distribution. The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon entropy. The normal distribution is recovered as q → 1. (en)
name	q-Gaussian (en)
foaf:depiction
dcterms:subject	Statistical mechanics Probability distributions with non-finite variance Continuous distributions
Wikipage page ID	32185446 (xsd:integer)
Wikipage revision ID	1123355647 (xsd:integer)
Link from a Wikipage to another Wikipage	Entropy (statistical thermodynamics) Degrees of freedom (statistics) Statistical mechanics Compact space Constantino Tsallis Q-Gaussian process Q-analog Q-exponential distribution Entropy (information theory) Geology Box–Muller transform Tsallis statistics Machine learning Student's t-distribution Central limit theorem White noise Anatomy Economics Normal distribution Probability distributions with non-finite variance Probability density function Tsallis entropy Random variable Statistical mechanics Astronomy Continuous distributions Finance Independent and identically distributed random variables Real number Heavy tails Tsallis distribution Nonextensive entropy Shape parameter Information entropy
Link from a Wikipage to an external page	http://e1.newcastle.edu.au/coffee/pubs/wp/2007/07-10.pdf http://www.cscs.umich.edu/~crshalizi/notebooks/tsallis.html
sameAs	Q-Gaussian distribution Q-Gaussian distribution Q-Gaussian distribution Q-Gaussian distribution Q-Gaussian distribution
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dbp:wikiPageUsesTemplate	dbt:About dbt:Citation_needed dbt:Cite_web dbt:ProbDistributions dbt:Reflist dbt:Short_description dbt:Probability_distribution dbt:Tsallis
thumbnail	wiki-commons:Special:FilePath/The_PDF_of_QGaussian.svg?width=300
type	density (en)
has abstract	The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints. It is one example of a Tsallis distribution. The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon entropy. The normal distribution is recovered as q → 1. The q-Gaussian has been applied to problems in the fields of statistical mechanics, geology, anatomy, astronomy, economics, finance, and machine learning. The distribution is often favored for its heavy tails in comparison to the Gaussian for 1 < q < 3. For the q-Gaussian distribution is the PDF of a bounded random variable. This makes in biology and other domains the q-Gaussian distribution more suitable than Gaussian distribution to model the effect of external stochasticity. A generalized q-analog of the classical central limit theorem was proposed in 2008, in which the independence constraint for the i.i.d. variables is relaxed to an extent defined by the q parameter, with independence being recovered as q → 1. However, a proof of such a theorem is still lacking. In the heavy tail regions, the distribution is equivalent to the Student's t-distribution with a direct mapping between q and the degrees of freedom. A practitioner using one of these distributions can therefore parameterize the same distribution in two different ways. The choice of the q-Gaussian form may arise if the system is non-extensive, or if there is lack of a connection to small samples sizes. (en) q-ガウス分布（英: q-Gaussian distribution）は、分散一定の条件下でを最大化して得られる確率分布。物理学者のコンスタンティーノ・ツァリスにより導出された。 (ja)
mean	, otherwise undefined (en)
parameters	shape (en)
pdf image	325 (xsd:integer)
prov:wasDerivedFrom	wikipedia-en:Q-Gaussian_distribution?oldid=1123355647&ns=0
page length (characters) of wiki page	12083 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Q-Gaussian_distribution
is Link from a Wikipage to another Wikipage of	List of q-analogs Q-Gaussian process List of statistics articles Tsallis distribution Q-Gaussian Q-gaussian
is Wikipage redirect of	Q-Gaussian Q-gaussian
is foaf:primaryTopic of	wikipedia-en:Q-Gaussian_distribution

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