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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.ExtremeValueDist
public class ExtremeValueDist
Extends the class ContinuousDistribution
for
the extreme value (or Gumbel) distribution, with location parameter
α and scale parameter
λ > 0.
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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ExtremeValueDist()
Constructs a ExtremeValueDist object with parameters α = 0 and λ = 1. |
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ExtremeValueDist(double alpha,
double lambda)
Constructs a ExtremeValueDist object with parameters α = alpha and λ = lambda. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double alpha,
double lambda,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double alpha,
double lambda,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double alpha,
double lambda,
double x)
Computes the density function. |
double |
getAlpha()
Returns the parameter α of this object. |
static ExtremeValueDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of an extreme value distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getLambda()
Returns the parameter λ of this object. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(α), hat(λ)] of the extreme value 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 alpha,
double lambda)
Computes and returns the mean, E[X] = α + γ/λ, of the extreme value distribution with parameters α and λ, where γ = 0.5772156649 is the Euler-Mascheroni constant. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha,
double lambda)
Computes and returns the standard deviation of the extreme value distribution with parameters α and λ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha,
double lambda)
Computes and returns the variance, Var[X] = π2/(6λ2), of the extreme value distribution with parameters α and λ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double alpha,
double lambda,
double u)
Computes the inverse distribution function. |
void |
setParams(double alpha,
double lambda)
Sets the parameters α and λ of this object. |
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 ExtremeValueDist()
public ExtremeValueDist(double alpha, double lambda)
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 alpha, double lambda, double x)
public static double cdf(double alpha, double lambda, double x)
public static double barF(double alpha, double lambda, double x)
public static double inverseF(double alpha, double lambda, double u)
public static ExtremeValueDist 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 alpha, double lambda)
public static double getVariance(double alpha, double lambda)
public static double getStandardDeviation(double alpha, double lambda)
public double getAlpha()
public double getLambda()
public void setParams(double alpha, double lambda)
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