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The Laplace Distribution
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The Laplace Distribution
The Laplace distribution is sometimes called the double
exponential distribution. It is used to model variables with a
distribution that is more heavy-taled than the normal
distribution.
The Laplace distribution has a location parameter corresponding
to the mean of the distribution, and a scale parameter. The
probability density function is:
The Laplace distribution is also known as the extreme value
distribution or the log-Weibull distribution.
The Laplace distribution is implemented by the LaplaceDistribution
class. It has three constructors. The first constructor has two
parameters. The first parameter is the location parameter, and
corresponds to the mode of the probability density function. The
second parameter is the scale parameter.
The following constructs the same Laplace distribution with
location parameter 6.8 and scale parameter 4.1:
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LaplaceDistribution laplace = new LaplaceDistribution(6.8, 4.1); |
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Dim laplace As LaplaceDistribution = New LaplaceDistribution(6.8, 4.1) |
If a variable is assumed to have a Laplace distribution, then
the parameter of the distribution can be estimated using the method
of matching moments. The second and third constructors perform this
calculation. The first parameter is a NumericalVariable
whose distribution is to be estimated. The optional second
parameter is a EstimationMethod
value that specifies the method to be used. The default is the
method of matching moments.
Note that parameter estimation says nothing about how well the
estimated distribution fits the variable's distribution. Use one of
the goodness-of-fit tests to verify the appropriateness of the
choice of distribution.
The LaplaceDistribution class has two specific
properties,
LocationParameter and
ScaleParameter, which return the location parameter
(mode) and scale parameter of the distribution.
LaplaceDistribution has one static (Shared
in Visual Basic) method,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator. The second
and third parameters are the location and scale parameters of the
distribution.
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MersenneTwister random = new MersenneTwister();
double variate = LaplaceDistribution.GetRandomVariate(random, 6.8, 4.1); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = LaplaceDistribution.GetRandomVariate(random, 6.8, 4.1) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Logistic Distribution Previous: The Gumbel Distribution Contents
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