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.

All labels observed (1)

Label Occurrences
q-Gaussian distribution canonical 2

How this entity was disambiguated

Statements (47)

Predicate Object
instanceOf Tsallis distribution ⓘ
generalized Gaussian distribution ⓘ
probability distribution ⓘ
arisesIn Tsallis statistics ⓘ
linked to: Tsallis
belongsTo non-Gaussian stable-like distributions ⓘ
generalizes normal distribution ⓘ
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 ⓘ
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 ⓘ

How these facts were elicited

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Tsallis → proposedConcept → q-Gaussian distribution ⓘ
Cauchy distribution → isSpecialCaseOf → q-Gaussian distribution ⓘ