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SSJ V. 1.2.5. |
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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.LaplaceDist
public class LaplaceDist
Extends the class ContinuousDistribution
for
the Laplace distribution.
It has location parameter θ and scale parameter φ > 0.
The density function is given by
F(x) = | (1/2)e(x-θ)/φ | if x <= θ, |
F(x) = | 1 - (1/2)e(θ-x)/φ | otherwise, |
F-1(u) = | φlog(2u) + θ | if 0 <= u <= 1/2, |
F-1(u) = | θ - φlog(2(1 - u)) | otherwise. |
Field Summary |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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LaplaceDist()
Constructs a LaplaceDist object with default parameters θ = 0 and φ = 1. |
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LaplaceDist(double theta,
double phi)
Constructs a LaplaceDist object with parameters θ = theta and φ = phi. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double theta,
double phi,
double x)
Computes the Laplace complementary distribution function. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double theta,
double phi,
double x)
Computes the Laplace distribution function. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double theta,
double phi,
double x)
Computes the Laplace density function. |
static LaplaceDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Laplace distribution with parameters θ and φ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(&thetas;), hat(&phis;)] of the Laplace distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(double theta,
double phi)
Computes and returns the mean E[X] = θ of the Laplace distribution with parameters θ and φ. |
double |
getPhi()
Returns the parameter φ. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double theta,
double phi)
Computes and returns the standard deviation of the Laplace distribution with parameters θ and φ. |
double |
getTheta()
Returns the parameter θ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double theta,
double phi)
Computes and returns the variance Var[X] = 2φ2 of the Laplace distribution with parameters θ and φ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double theta,
double phi,
double u)
Computes the inverse Laplace distribution function. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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inverseBisection, inverseBrent |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public LaplaceDist()
public LaplaceDist(double theta, double phi)
Method Detail |
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public double density(double x)
ContinuousDistribution
density
in class ContinuousDistribution
x
- value at which the density is evaluated
public double cdf(double x)
Distribution
x
- value at which the distribution function is evaluated
public double barF(double x)
Distribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary distribution function is evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
u
- value in the interval (0, 1) for which the inverse
distribution function is evaluated
public double getMean()
Distribution
public double getVariance()
Distribution
public double getStandardDeviation()
Distribution
public static double density(double theta, double phi, double x)
public static double cdf(double theta, double phi, double x)
public static double barF(double theta, double phi, double x)
public static double inverseF(double theta, double phi, double u)
public static LaplaceDist getInstanceFromMLE(double[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(double[] x, int n)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parameters
public static double getMean(double theta, double phi)
public static double getVariance(double theta, double phi)
public static double getStandardDeviation(double theta, double phi)
public double getTheta()
public double getPhi()
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SSJ V. 1.2.5. |
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