Laplace distribution
E628628
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 (44)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
univariate probability distribution ⓘ |
| alsoKnownAs | double exponential distribution NERFINISHED ⓘ |
| belongsTo | location-scale distributions ⓘ |
| belongsToFamily |
generalized error distributions
ⓘ
subbotin distributions NERFINISHED ⓘ |
| characteristicFunction | φ(t) = 1 / (1 + b^2 t^2) ⓘ |
| cumulativeDistributionFunction |
F(x|μ,b) = 0.5 exp((x-μ)/b) for x < μ
ⓘ
F(x|μ,b) = 1 - 0.5 exp(-(x-μ)/b) for x ≥ μ ⓘ |
| entropy | 1 + ln(2b) ⓘ |
| excessKurtosis | 3 ⓘ |
| hasHeavierTailsThan | normal distribution ⓘ |
| hasLogLikelihood | proportional to negative L1 norm of residuals ⓘ |
| hasParameter |
location parameter μ
ⓘ
scale parameter b ⓘ |
| hasProbabilityDensityFunctionProperty | piecewise exponential around μ ⓘ |
| isDifferenceOf | two independent exponential distributions with same rate ⓘ |
| isScaleMixtureOf | normal distributions ⓘ |
| isSymmetricAbout | μ ⓘ |
| isUsedIn |
differential privacy mechanisms
ⓘ
financial return modeling with jumps ⓘ signal and image processing ⓘ |
| kurtosis | 6 ⓘ |
| lossFunctionConnection | corresponds to L1 loss in maximum likelihood estimation ⓘ |
| mean | μ ⓘ |
| median | μ ⓘ |
| mode | μ ⓘ |
| momentGeneratingFunction | M(t) = 1 / (1 - b^2 t^2) for |t| < 1/b ⓘ |
| namedAfter | Pierre-Simon Laplace NERFINISHED ⓘ |
| peakShape | sharper peak at mean than normal distribution ⓘ |
| probabilityDensityFunction | f(x|μ,b) = (1/(2b)) exp(-|x-μ|/b) ⓘ |
| skewness | 0 ⓘ |
| specialCaseOf |
asymmetric Laplace distribution
ⓘ
generalized Laplace distribution ⓘ |
| support | all real numbers ⓘ |
| supportLowerBound | -∞ ⓘ |
| supportUpperBound | +∞ ⓘ |
| tailBehavior | exponential tails ⓘ |
| usedFor |
Bayesian L1 regularization priors
ⓘ
modeling abrupt changes ⓘ modeling data with outliers ⓘ robust regression error modeling ⓘ sparse signal modeling ⓘ |
| variance | 2 b^2 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.