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java.lang.Objectumontreal.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 bar(F)(x) = 1 - F(x). |
static double |
barF(double alpha,
double beta,
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 beta,
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 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 in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(α), hat(β)] of the Pareto 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 beta)
Computes and returns the mean E[X] = αβ/(α - 1) of the Pareto distribution with parameters α and β. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
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 of the distribution function. |
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)
Computes and returns the inverse distribution function F-1(u), defined in. |
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. |
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 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)
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 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 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[] 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 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)
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