LaplaceDistribution

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:

Moment:

Closed form for symbolic order:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Closed form for symbolic order:

Hazard function:

Quantile function:

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: