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java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.GumbelDist
public class GumbelDist
Extends the class ContinuousDistribution
for
the Gumbel distribution, with location parameter
δ and scale parameter
β≠ 0. Using the notation
z = (x - δ)/β,
it has density
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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GumbelDist()
Constructor for the standard Gumbel distribution with parameters β = 1 and δ = 0. |
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GumbelDist(double beta,
double delta)
Constructs a GumbelDist object with parameters β = beta and δ = delta. |
Method Summary | |
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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. |
String |
toString()
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Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
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public GumbelDist()
public GumbelDist(double beta, double delta)
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)
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 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 parameters
public 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 parameters
public 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 String toString()
toString
in class Object
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