C# Class Accord.Statistics.Distributions.Univariate.LaplaceDistribution

Laplace's Distribution (as known as the double exponential distribution).

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution.

The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.

The probability density function of the Laplace distribution is also reminiscent of the normal distribution; however, whereas the normal distribution is expressed in terms of the squared difference from the mean μ, the Laplace density is expressed in terms of the absolute difference from the mean. Consequently the Laplace distribution has fatter tails than the normal distribution.

References: Wikipedia, The Free Encyclopedia. Laplace distribution. Available from: http://en.wikipedia.org/wiki/Laplace_distribution

Inheritance: UnivariateContinuousDistribution, IFormattable

Show file Open project: accord-net/framework Class Usage Examples

Public Methods

Method	Description
Clone ( ) : object	Creates a new object that is a copy of the current instance.
DistributionFunction ( double x ) : double	Gets the cumulative distribution function (cdf) for this distribution evaluated at point `x`. The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
LaplaceDistribution ( [ location, [ scale ) : System	Creates a new Laplace distribution.
LogProbabilityDensityFunction ( double x ) : double	Gets the log-probability density function (pdf) for this distribution evaluated at point `x`. The Probability Density Function (PDF) describes the probability that a given value `x` will occur.
ProbabilityDensityFunction ( double x ) : double	Gets the probability density function (pdf) for this distribution evaluated at point `x`. The Probability Density Function (PDF) describes the probability that a given value `x` will occur.
ToString ( string format, IFormatProvider formatProvider ) : string	Returns a System.String that represents this instance.

Method Details

Clone() public method

Creates a new object that is a copy of the current instance.

public Clone ( ) : object
return	object

DistributionFunction() public method

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.

The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.

public DistributionFunction ( double x ) : double
x	double	A single point in the distribution range.
return	double

LaplaceDistribution() public method

Creates a new Laplace distribution.

public LaplaceDistribution ( [ location, [ scale ) : System
location	[	The location parameter μ (mu).
scale	[	The scale parameter b.
return	System

LogProbabilityDensityFunction() public method

Gets the log-probability density function (pdf) for this distribution evaluated at point x.

The Probability Density Function (PDF) describes the probability that a given value x will occur.

public LogProbabilityDensityFunction ( double x ) : double
x	double	A single point in the distribution range.
return	double

ProbabilityDensityFunction() public method

Gets the probability density function (pdf) for this distribution evaluated at point x.

The Probability Density Function (PDF) describes the probability that a given value x will occur.

public ProbabilityDensityFunction ( double x ) : double
x	double	A single point in the distribution range.
return	double

ToString() public method

Returns a System.String that represents this instance.

public ToString ( string format, IFormatProvider formatProvider ) : string
format	string
formatProvider	IFormatProvider
return	string