|
SSJ V. 2.6. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.LaplaceDist
public class LaplaceDist
Extends the class ContinuousDistribution
for
the Laplace distribution.
It has location parameter μ and scale parameter β > 0.
The density function is given by
F(x) = | (1/2)e(x-μ)/β | if x <= μ, |
F(x) = | 1 - (1/2)e(μ-x)/β | otherwise, |
F-1(u) = | βlog(2u) + μ | if 0 <= u <= 1/2, |
F-1(u) = | μ - βlog(2(1 - u)) | otherwise. |
Field Summary |
---|
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
---|
decPrec |
Constructor Summary | |
---|---|
LaplaceDist()
Constructs a LaplaceDist object with default parameters μ = 0 and β = 1. |
|
LaplaceDist(double mu,
double beta)
Constructs a LaplaceDist object with parameters μ = mu and β = beta. |
Method Summary | |
---|---|
double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double mu,
double beta,
double x)
Computes the Laplace complementary distribution function. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double mu,
double beta,
double x)
Computes the Laplace distribution function. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double mu,
double beta,
double x)
Computes the Laplace density function. |
double |
getBeta()
Returns the parameter β. |
static LaplaceDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Laplace distribution with parameters μ and β estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean. |
static double |
getMean(double mu,
double beta)
Computes and returns the mean E[X] = μ of the Laplace distribution with parameters μ and β. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (μ, β) of the Laplace distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double |
getMu()
Returns the parameter μ. |
double[] |
getParams()
Return a table containing the parameters of the current distribution. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double mu,
double beta)
Computes and returns the standard deviation of the Laplace distribution with parameters μ and β. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double mu,
double beta)
Computes and returns the variance Var[X] = 2β2 of the Laplace distribution with parameters μ and β. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double mu,
double beta,
double u)
Computes the inverse Laplace distribution function. |
String |
toString()
|
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
---|
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup |
Methods inherited from class java.lang.Object |
---|
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
---|
public LaplaceDist()
public LaplaceDist(double mu, double beta)
Method Detail |
---|
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)
ContinuousDistribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary distribution function is evaluated
public double inverseF(double u)
ContinuousDistribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
u
- value at which the inverse distribution function is evaluated
public double getMean()
ContinuousDistribution
getMean
in interface Distribution
getMean
in class ContinuousDistribution
public double getVariance()
ContinuousDistribution
getVariance
in interface Distribution
getVariance
in class ContinuousDistribution
public double getStandardDeviation()
ContinuousDistribution
getStandardDeviation
in interface Distribution
getStandardDeviation
in class ContinuousDistribution
public static double density(double mu, double beta, double x)
public static double cdf(double mu, double beta, double x)
public static double barF(double mu, double beta, double x)
public static double inverseF(double mu, double beta, double u)
public static double[] getMLE(double[] x, int n)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parameters
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 getMean(double mu, double beta)
public static double getVariance(double mu, double beta)
public static double getStandardDeviation(double mu, double beta)
public double getMu()
public double getBeta()
public double[] getParams()
public String toString()
toString
in class Object
|
SSJ V. 2.6. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |