SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class PowerDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.PowerDist
All Implemented Interfaces:
Distribution

public class PowerDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the power distribution with shape parameter c > 0, over the interval [a, b], where a < b. It has density

f (x) = c(x - a)c-1/(b - a)c

for a < x < b, and 0 elsewhere. It has distribution function

F(x) = (x - a)c/(b - a)c        for a <= x <= b,

with F(x) = 0 for x <= a and F(x) = 1 for x >= b.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
PowerDist(double c)
          Constructs a PowerDist object with parameters a = 0, b = 1 and c = c.
PowerDist(double b, double c)
          Constructs a PowerDist object with parameters a = 0, b = b and c = c.
PowerDist(double a, double b, double c)
          Constructs a PowerDist object with parameters a = a, b = b and c = c.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double a, double b, double c, double x)
          Computes the complementary distribution function.
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(double a, double b, double c, double x)
          Computes the distribution function.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double a, double b, double c, double x)
          Computes the density function.
 double getA()
          Returns the parameter a.
 double getB()
          Returns the parameter b.
 double getC()
          Returns the parameter c.
static PowerDist getInstanceFromMLE(double[] x, int n, double a, double b)
          Creates a new instance of a power distribution with parameters a and b, with c estimated using the maximum likelihood method based on the n observations x[i], i = 0,…, n - 1.
 double getMean()
          Returns the mean.
static double getMean(double a, double b, double c)
          Returns the mean a + (b - a)c/(c + 1) of the power distribution with parameters a, b and c.
static double[] getMLE(double[] x, int n, double a, double b)
          Estimates the parameter c of the power distribution from the n observations x[i], i = 0, 1,…, n - 1, using the maximum likelihood method and assuming that a and b are known.
 double[] getParams()
          Return a table containing the parameters of the current distribution.
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double a, double b, double c)
          Computes and returns the standard deviation of the power distribution with parameters a, b and c.
 double getVariance()
          Returns the variance.
static double getVariance(double a, double b, double c)
          Computes and returns the variance (b - a)2c/[(c + 1)2(c + 2)] of the power distribution with parameters a, b and c.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double a, double b, double c, double u)
          Computes the inverse of the distribution function.
 void setParams(double a, double b, double c)
          Sets the parameters a, b and c for this object.
 String toString()
           
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

PowerDist

public PowerDist(double a,
                 double b,
                 double c)
Constructs a PowerDist object with parameters a = a, b = b and c = c.


PowerDist

public PowerDist(double b,
                 double c)
Constructs a PowerDist object with parameters a = 0, b = b and c = c.


PowerDist

public PowerDist(double c)
Constructs a PowerDist object with parameters a = 0, b = 1 and c = c.

Method Detail

density

public double density(double x)
Description copied from class: ContinuousDistribution
Returns f (x), the density evaluated at x.

Specified by:
density in class ContinuousDistribution
Parameters:
x - value at which the density is evaluated
Returns:
density function evaluated at x

cdf

public double cdf(double x)
Description copied from interface: Distribution
Returns the distribution function F(x).

Parameters:
x - value at which the distribution function is evaluated
Returns:
distribution function evaluated at x

barF

public double barF(double x)
Description copied from class: ContinuousDistribution
Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:
barF in interface Distribution
Overrides:
barF in class ContinuousDistribution
Parameters:
x - value at which the complementary distribution function is evaluated
Returns:
complementary distribution function evaluated at x

inverseF

public double inverseF(double u)
Description copied from class: ContinuousDistribution
Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from class: ContinuousDistribution
Returns the mean.

Specified by:
getMean in interface Distribution
Overrides:
getMean in class ContinuousDistribution
Returns:
the mean

getVariance

public double getVariance()
Description copied from class: ContinuousDistribution
Returns the variance.

Specified by:
getVariance in interface Distribution
Overrides:
getVariance in class ContinuousDistribution
Returns:
the variance

getStandardDeviation

public double getStandardDeviation()
Description copied from class: ContinuousDistribution
Returns the standard deviation.

Specified by:
getStandardDeviation in interface Distribution
Overrides:
getStandardDeviation in class ContinuousDistribution
Returns:
the standard deviation

density

public static double density(double a,
                             double b,
                             double c,
                             double x)
Computes the density function.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
x - the value at which the density is evaluated
Returns:
returns the density function

cdf

public static double cdf(double a,
                         double b,
                         double c,
                         double x)
Computes the distribution function.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
x - the value at which the distribution is evaluated
Returns:
returns the distribution function

barF

public static double barF(double a,
                          double b,
                          double c,
                          double x)
Computes the complementary distribution function.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
x - the value at which the complementary distribution is evaluated
Returns:
returns the complementary distribution function

inverseF

public static double inverseF(double a,
                              double b,
                              double c,
                              double u)
Computes the inverse of the distribution function.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
u - the value at which the inverse distribution is evaluated
Returns:
returns the inverse of the distribution function

getMLE

public static double[] getMLE(double[] x,
                              int n,
                              double a,
                              double b)
Estimates the parameter c of the power distribution from the n observations x[i], i = 0, 1,…, n - 1, using the maximum likelihood method and assuming that a and b are known. The estimate is returned in a one-element array: [c].

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters
a - left limit of interval
b - right limit of interval
Returns:
returns the shape parameter [hat(c)]

getInstanceFromMLE

public static PowerDist getInstanceFromMLE(double[] x,
                                           int n,
                                           double a,
                                           double b)
Creates a new instance of a power distribution with parameters a and b, with c estimated using the maximum likelihood method based on the n observations x[i], i = 0,…, n - 1.

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters
a - left limit of interval
b - right limit of interval

getMean

public static double getMean(double a,
                             double b,
                             double c)
Returns the mean a + (b - a)c/(c + 1) of the power distribution with parameters a, b and c.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
Returns:
returns the mean

getVariance

public static double getVariance(double a,
                                 double b,
                                 double c)
Computes and returns the variance (b - a)2c/[(c + 1)2(c + 2)] of the power distribution with parameters a, b and c.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter
Returns:
returns the variance

getStandardDeviation

public static double getStandardDeviation(double a,
                                          double b,
                                          double c)
Computes and returns the standard deviation of the power distribution with parameters a, b and c.

Returns:
the standard deviation of the power distribution

getA

public double getA()
Returns the parameter a.

Returns:
the left limit of interval a

getB

public double getB()
Returns the parameter b.

Returns:
the right limit of interval b

getC

public double getC()
Returns the parameter c.

Returns:
the shape parameter c

setParams

public void setParams(double a,
                      double b,
                      double c)
Sets the parameters a, b and c for this object.

Parameters:
a - left limit of interval
b - right limit of interval
c - shape parameter

getParams

public double[] getParams()
Return a table containing the parameters of the current distribution. This table is put in regular order: [a, b, c].

Returns:
[a, b,c]

toString

public String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.