q-Gaussian distribution
E809119
The q-Gaussian distribution is a generalized probability distribution arising in Tsallis statistics that extends the normal (Gaussian) distribution to model systems with heavy tails and nonextensive behavior.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Tsallis distribution
ⓘ
generalized Gaussian distribution ⓘ probability distribution ⓘ |
| arisesIn | Tsallis statistics NERFINISHED ⓘ |
| belongsTo | non-Gaussian stable-like distributions ⓘ |
| generalizes | normal distribution NERFINISHED ⓘ |
| hasFamilyName | q-Gaussian family ⓘ |
| hasFiniteMeanCondition | q < 2 ⓘ |
| hasFiniteVarianceCondition | q < 5/3 ⓘ |
| hasInfiniteMean | for 2 ≤ q < 3 ⓘ |
| hasInfiniteVariance | for 5/3 ≤ q < 3 ⓘ |
| hasLimitingCase | uniform distribution as q → -∞ (in a bounded domain, formal) ⓘ |
| hasParameter |
location parameter
ⓘ
q ⓘ scale parameter ⓘ |
| hasShapeParameter | q ⓘ |
| hasSupport |
bounded support for q < 1
ⓘ
unbounded support for 1 ≤ q < 3 ⓘ |
| hasTailBehavior |
Gaussian tails for q = 1
ⓘ
compact support for q < 1 ⓘ power-law tails for 1 < q < 3 ⓘ |
| isAlternativeTo | Student-t distribution for heavy tails ⓘ |
| isAssociatedWith | Tsallis entropy NERFINISHED ⓘ |
| isBasedOn | nonextensive statistical mechanics ⓘ |
| isConnectedTo | central limit theorems in nonextensive statistics ⓘ |
| isDefinedOn | real line ⓘ |
| isEvenFunction | true ⓘ |
| isNonNormalizableFor | q ≥ 3 ⓘ |
| isNormalizableFor | q < 3 ⓘ |
| isParameterizedBy | entropic index q ⓘ |
| isRelatedTo |
q-exponential function
ⓘ
q-logarithm ⓘ |
| isSpecialCaseOf | q-exponential family ⓘ |
| isSymmetric | true ⓘ |
| isUnimodal | true ⓘ |
| isUsedIn |
complex systems theory
ⓘ
econophysics ⓘ plasma physics ⓘ statistical physics ⓘ turbulence modeling ⓘ |
| isUsedToModel |
anomalous diffusion
ⓘ
heavy-tailed phenomena ⓘ nonextensive systems ⓘ systems with long-range interactions ⓘ systems with long-term memory ⓘ |
| maximizes | Tsallis entropy under suitable constraints ⓘ |
| reducesTo | normal distribution when q = 1 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.