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java.lang.Object umontreal.iro.lecuyer.probdist.ContinuousDistribution umontreal.iro.lecuyer.probdist.ParetoDist
public class ParetoDist
Extends the class ContinuousDistribution
for a distribution
from the Pareto family, with
shape parameter
α > 0 and location parameter β > 0.
The density for this type of Pareto distribution is
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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ParetoDist(double alpha)
Constructs a ParetoDist object with parameters α = alpha and β = 1. |
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ParetoDist(double alpha,
double beta)
Constructs a ParetoDist object with parameters α = alpha and β = beta. |
Method Summary | |
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double |
barF(double x)
Returns the complementary distribution function. |
static double |
barF(double alpha,
double beta,
double x)
Computes the complementary distribution function. |
double |
cdf(double x)
Returns the distribution function F(x). |
static double |
cdf(double alpha,
double beta,
double x)
Computes the distribution function. |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double alpha,
double beta,
double x)
Computes the density function. |
double |
getAlpha()
Returns the parameter α. |
double |
getBeta()
Returns the parameter β. |
static ParetoDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a Pareto distribution with parameters α 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 alpha,
double beta)
Computes and returns the mean E[X] = αβ/(α - 1) of the Pareto distribution with parameters α and β. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (α, β) of the Pareto distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double[] |
getParams()
Return a table containing the parameters of the current distribution. |
double |
getStandardDeviation()
Returns the standard deviation. |
static double |
getStandardDeviation(double alpha,
double beta)
Computes and returns the standard deviation of the Pareto distribution with parameters α and β. |
double |
getVariance()
Returns the variance. |
static double |
getVariance(double alpha,
double beta)
Computes and returns the variance of the Pareto distribution with parameters α and β. |
double |
inverseF(double u)
Returns the inverse distribution function x = F-1(u). |
static double |
inverseF(double alpha,
double beta,
double u)
Computes the inverse of the distribution function. |
void |
setParams(double alpha,
double beta)
Sets the parameter α and β for 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 ParetoDist(double alpha)
public ParetoDist(double alpha, double beta)
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 alpha, double beta, double x)
public static double cdf(double alpha, double beta, double x)
public static double barF(double alpha, double beta, double x)
public static double inverseF(double alpha, 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 ParetoDist 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 alpha, double beta)
public static double getVariance(double alpha, double beta)
public static double getStandardDeviation(double alpha, double beta)
public double getAlpha()
public double getBeta()
public void setParams(double alpha, double beta)
public double[] getParams()
public String toString()
toString
in class Object
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