LaplaceDistribution

The Laplace (double-exponential) distribution with location $\mu$ and scale $b$.

LaplaceDistribution(mu, b)an inert distribution object — carries $\mu, b$, unevaluated.

Typed signatures

Type	Package	Applies
(real, real<0..>) -> distribution	statistics	always

Domain: Statistics

Details

• $PDF(x) = e^{-|x-\mu|/b}/(2b)$, exact.
• $CDF(x) = e^{(x-\mu)/b}/2$ for $x < \mu$, $1-e^{-(x-\mu)/b}/2$ otherwise.
• $Mean = \mu$, $Variance = 2b^2$, both exact.
• RandomVariate samples via inverse transform.

Examples

Basic #

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In$\operatorname{PDF}(\mathrm{LaplaceDistribution}(0, \frac{1}{2}), 0)$Out$1$

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In$\operatorname{CDF}(\mathrm{LaplaceDistribution}(0, \frac{1}{2}), 0)$Out$\frac{1}{2}$

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In$\mathrm{mean}(\mathrm{LaplaceDistribution}(0, \frac{1}{2}))$Out$0$

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In$\mathrm{Variance}(\mathrm{LaplaceDistribution}(0, \frac{1}{2}))$Out$\frac{1}{2}$

About

Examples	4

See also: CauchyDistribution, LogisticDistribution, PDF, CDF