SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class PiecewiseLinearEmpiricalDist

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

public class PiecewiseLinearEmpiricalDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for a piecewise-linear approximation of the empirical distribution function, based on the observations X(1),..., X(n) (sorted by increasing order), and defined as follows (e.g.,). The distribution function starts at X(1) and climbs linearly by 1/(n - 1) between any two successive observations. The density is

f (x) = 1/[(n - 1)(X(i+1) - X(i))] for X(i) <= x < X(i+1) and i = 1, 2,..., n - 1.

The distribution function is

F(x) = 0          for x < X(1),
F(x) = (i - 1)/(n - 1) + (x - X(i))/[(n - 1)(X(i+1) - X(i))]          for X(i) <= x < X(i+1),
F(x) = 1          elsewhere,

whose inverse is

F-1(u) = X(i) + ((n - 1)u - i + 1)(X(i+1) - X(i))

for (i - 1)/(n - 1) <= u <= i/(n - 1) and i = 1,..., n - 1.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
PiecewiseLinearEmpiricalDist(double[] obs)
          Constructs a new piecewise-linear distribution using all the observations stored in obs.
PiecewiseLinearEmpiricalDist(Reader in)
          Constructs a new empirical distribution using the observations read from the reader in.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
 double cdf(double x)
          Returns the distribution function F(x).
 double density(double x)
          Returns f (x), the density evaluated at x.
 double getMean()
          Returns the mean.
 int getN()
          Returns n, the number of observations.
 double getObs(int i)
          Returns the value of X(i).
 double[] getParams()
          Return a table containing parameters of the current distribution.
 double getSampleMean()
          Returns the sample mean of the observations.
 double getSampleStandardDeviation()
          Returns the sample standard deviation of the observations.
 double getSampleVariance()
          Returns the sample variance of the observations.
 double getStandardDeviation()
          Returns the standard deviation.
 double getVariance()
          Returns the variance.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
 String toString()
          Returns a String containing information about the current distribution.
 
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

PiecewiseLinearEmpiricalDist

public PiecewiseLinearEmpiricalDist(double[] obs)
Constructs a new piecewise-linear distribution using all the observations stored in obs. These observations are copied into an internal array and then sorted.


PiecewiseLinearEmpiricalDist

public PiecewiseLinearEmpiricalDist(Reader in)
                             throws IOException
Constructs a new empirical distribution using the observations read from the reader in. This constructor will read the first double of each line in the stream. Any line that does not start with a +, -, or a decimal digit, is ignored. The file is read until its end. One must be careful about lines starting with a blank. This format is the same as in UNURAN.

Throws:
IOException
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

getN

public int getN()
Returns n, the number of observations.


getObs

public double getObs(int i)
Returns the value of X(i).


getSampleMean

public double getSampleMean()
Returns the sample mean of the observations.


getSampleVariance

public double getSampleVariance()
Returns the sample variance of the observations.


getSampleStandardDeviation

public double getSampleStandardDeviation()
Returns the sample standard deviation of the observations.


getParams

public double[] getParams()
Return a table containing parameters of the current distribution.


toString

public String toString()
Returns a String containing information about the current distribution.

Overrides:
toString in class Object

SSJ
V. 2.6.

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