public class GumbelDist extends ContinuousDistribution
ContinuousDistribution for
the Gumbel distribution, with location parameter
δ and scale parameter
β≠ 0. Using the notation
z = (x - δ)/β,
it has density
decPrec| Constructor and Description |
|---|
GumbelDist()
Constructor for the standard
Gumbel distribution with parameters β = 1 and δ = 0.
|
GumbelDist(double beta,
double delta)
Constructs a GumbelDist object with parameters
β = beta and δ = delta.
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| Modifier and Type | Method and Description |
|---|---|
double |
barF(double x)
Returns the complementary distribution function.
|
static double |
barF(double beta,
double delta,
double x)
Computes and returns the complementary distribution function 1 - F(x).
|
double |
cdf(double x)
Returns the distribution function F(x).
|
static double |
cdf(double beta,
double delta,
double x)
Computes and returns the distribution function.
|
double |
density(double x)
Returns f (x), the density evaluated at x.
|
static double |
density(double beta,
double delta,
double x)
Computes and returns the density function.
|
double |
getBeta()
Returns the parameter β of this object.
|
double |
getDelta()
Returns the parameter δ of this object.
|
static GumbelDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of an Gumbel distribution with parameters
β and δ estimated using the maximum likelihood method based
on the n observations x[i],
i = 0, 1,…, n - 1, assuming that β > 0.
|
static GumbelDist |
getInstanceFromMLEmin(double[] x,
int n)
Similar to
getInstanceFromMLE, but for the case β < 0. |
double |
getMean()
Returns the mean.
|
static double |
getMean(double beta,
double delta)
Returns the mean,
E[X] = δ + γβ,
of the Gumbel distribution with parameters β and δ,
where
γ = 0.5772156649015329 is the Euler-Mascheroni constant.
|
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters
(β, δ) of the Gumbel distribution,
assuming that β > 0, and
using the maximum likelihood method with the n observations
x[i],
i = 0, 1,…, n - 1.
|
static double[] |
getMLEmin(double[] x,
int n)
Similar to
getMLE, but for the case β < 0. |
double[] |
getParams()
Return a table containing the parameters of the current distribution.
|
double |
getStandardDeviation()
Returns the standard deviation.
|
static double |
getStandardDeviation(double beta,
double delta)
Returns the standard deviation
of the Gumbel distribution with parameters β and δ.
|
double |
getVariance()
Returns the variance.
|
static double |
getVariance(double beta,
double delta)
Returns the variance
Var[X] = π2β2/6 of the Gumbel distribution with parameters β and δ.
|
double |
inverseF(double u)
Returns the inverse distribution function
x = F-1(u).
|
static double |
inverseF(double beta,
double delta,
double u)
Computes and returns the inverse distribution function.
|
void |
setParams(double beta,
double delta)
Sets the parameters β and δ of this object.
|
java.lang.String |
toString() |
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsuppublic GumbelDist()
public GumbelDist(double beta,
double delta)
public double density(double x)
ContinuousDistributiondensity in class ContinuousDistributionx - value at which the density is evaluatedpublic double cdf(double x)
Distributionx - value at which the distribution function is evaluatedpublic double barF(double x)
ContinuousDistributionbarF in interface DistributionbarF in class ContinuousDistributionx - value at which the complementary distribution function is evaluatedpublic double inverseF(double u)
ContinuousDistributioninverseF in interface DistributioninverseF in class ContinuousDistributionu - value at which the inverse distribution function is evaluatedpublic double getMean()
ContinuousDistributiongetMean in interface DistributiongetMean in class ContinuousDistributionpublic double getVariance()
ContinuousDistributiongetVariance in interface DistributiongetVariance in class ContinuousDistributionpublic double getStandardDeviation()
ContinuousDistributiongetStandardDeviation in interface DistributiongetStandardDeviation in class ContinuousDistributionpublic static double density(double beta,
double delta,
double x)
public static double cdf(double beta,
double delta,
double x)
public static double barF(double beta,
double delta,
double x)
public static double inverseF(double beta,
double delta,
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 parameterspublic static double[] getMLEmin(double[] x,
int n)
getMLE, but for the case β < 0.x - the list of observations used to evaluate parametersn - the number of observations used to evaluate parameterspublic static GumbelDist 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 GumbelDist getInstanceFromMLEmin(double[] x, int n)
getInstanceFromMLE, but for the case β < 0.x - the list of observations to use to evaluate parametersn - the number of observations to use to evaluate parameterspublic static double getMean(double beta,
double delta)
public static double getVariance(double beta,
double delta)
public static double getStandardDeviation(double beta,
double delta)
public double getBeta()
public double getDelta()
public void setParams(double beta,
double delta)
public double[] getParams()
public java.lang.String toString()
toString in class java.lang.ObjectTo submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.