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LaplaceDistribution

LaplaceDistribution[Mu, Beta]
represents a Laplace double-exponential distribution with mean Mu and scale parameter Beta.
  • The Laplace distribution gives the distribution of the difference between two independent random variables with identical exponential distributions.
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Basic Examples   (2)
The mean and variance of a Laplace distribution:
Probability density function:
The mean and variance of a Laplace distribution:
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Probability density function:
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Scope   (3)
Generate a set of pseudorandom numbers that are Laplace distributed:
Properties based on higher-order moments:
The q^(th) quantile of a Laplace distribution:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and Beta are varied:
Properties & Relations   (3)
The probability density function integrates to unity:
Moments can be obtained from the characteristic function:
Halves of the distribution are proportional to ExponentialDistribution densities:
Possible Issues   (2)
LaplaceDistribution is not defined when Mu is not a real number:
LaplaceDistribution is not defined when Beta is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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