double exponential distribution
E628629
The double exponential distribution, also known as the Laplace distribution, is a continuous probability distribution with a sharp peak at its mean and heavier tails than the normal distribution, often used to model data with abrupt changes or outliers.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf | probability distribution ⓘ |
| alsoKnownAs |
Laplace distribution
NERFINISHED
ⓘ
two-sided exponential distribution ⓘ |
| belongsToFamily |
exponential family
ⓘ
location-scale family ⓘ |
| canBeRepresentedAs | scale mixture of normals with exponential mixing distribution ⓘ |
| hasCharacteristicFunction | φ(t) = exp(i μ t) / (1 + b^2 t^2) ⓘ |
| hasCumulativeDistributionFunction |
F(x) = 0.5 exp((x-μ)/b) for x < μ
ⓘ
F(x) = 1 - 0.5 exp(-(x-μ)/b) for x ≥ μ ⓘ |
| hasEntropy | 1 + ln(2b) ⓘ |
| hasExcessKurtosis | 3 ⓘ |
| hasFiniteMomentsOfAllOrders | true ⓘ |
| hasFisherInformationForLocation | 1/b^2 ⓘ |
| hasFisherInformationForScale | 2/b^2 ⓘ |
| hasHazardFunction | h(x) = f(x) / S(x) ⓘ |
| hasHeavierTailsThan | normal distribution ⓘ |
| hasKurtosis | 6 ⓘ |
| hasLocationParameter | μ ⓘ |
| hasLogConcaveDensity | true ⓘ |
| hasMean | μ ⓘ |
| hasMedian | μ ⓘ |
| hasMode | μ ⓘ |
| hasMomentGeneratingFunction | M(t) = exp(μ t) / (1 - b^2 t^2), |t| < 1/b ⓘ |
| hasProbabilityDensityFunction |
f(x|μ,b) = (1/(2b)) exp(-|x-μ|/b)
ⓘ
f(x|μ,λ) = (λ/2) exp(-λ|x-μ|) ⓘ |
| hasRateParameterization | b = 1/λ ⓘ |
| hasScaleParameter | b ⓘ |
| hasSharperPeakThan | normal distribution ⓘ |
| hasSkewness | 0 ⓘ |
| hasStandardDeviation | √2 b ⓘ |
| hasSupport | (-∞, ∞) ⓘ |
| hasSurvivalFunction | S(x) = 1 - F(x) ⓘ |
| hasVariance | 2 b^2 ⓘ |
| isInfinitelyDivisible | true ⓘ |
| isLimitOf | difference of two independent exponential variables with same rate ⓘ |
| isNamedAfter | Pierre-Simon Laplace NERFINISHED ⓘ |
| isSubexponential | false ⓘ |
| isSymmetricAbout | μ ⓘ |
| isUsedFor |
Bayesian L1 regularization priors
ⓘ
modeling data with heavy tails ⓘ modeling data with sharp peaks ⓘ modeling outliers ⓘ robust regression error modeling ⓘ |
| isUsedIn |
econometrics
ⓘ
image processing ⓘ signal processing ⓘ sparse Bayesian learning ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.