This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# LaplaceDistribution

 LaplaceDistribution represents a Laplace double-exponential distribution with mean and scale parameter .
• The Laplace distribution gives the distribution of the difference between two independent random variables with identical exponential distributions.
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
 Out[1]=
 Out[2]=

Cumulative distribution function:
 Out[1]=
 Out[2]=

Mean and variance:
 Out[1]=
 Out[2]=

Median:
 Out[1]=
 Scope   (6)
Generate a set of pseudorandom numbers that are Laplace distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness and kurtosis of Laplace distribution are constant:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
Data packets are arriving via two channels. Waiting times for each channel are exponentially distributed with the same parameter . Find the distribution of the waiting time between packets:
Find the probability of waiting time between the packets to be greater than 6 seconds:
Simulate waiting times between packets coming from both channels:
The difference of flood stages between river stations A and B in a year has been estimated to follow a Laplace distribution with and . Find the probability that the difference is greater than 15:
Find the probability of positive difference:
Find the mean and standard deviation of the difference of flood stages:
Simulate the differences of flood stages for 30 years:
Parameter influence on the CDF for each :
Laplace distribution is closed under translation and scaling by a positive factor:
Relationships to other distributions:
Halves of a Laplace distribution are proportional to ExponentialDistribution densities:
For negative argument:
The difference of two variates from ExponentialDistribution follows Laplace distribution:
ExponentialDistribution is a transformation of Laplace distribution:
Laplace distribution is a special case of ExponentialPowerDistribution:
If , , , and are independent and are normally distributed, then is Laplace distributed:
If , , , and are independent and are normally distributed, then is Laplace distributed:
ChiSquareDistribution is a transformation of Laplace distribution:
For the sum of such variables:
FRatioDistribution is a transformation of Laplace distribution:
Laplace distribution is a transformation of UniformDistribution:
LaplaceDistribution is the limiting case of HyperbolicDistribution of when and :
Laplace distribution is a parameter mixture of a NormalDistribution with RayleighDistribution:
LaplaceDistribution is not defined when is not a real number:
LaplaceDistribution is not defined when is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
New in 6