SSJ
V. 1.2.5.

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 bar(F)(x) = 1 - F(x).
 double cdf(double x)
          Computes and returns the distribution function F(x).
 double density(double x)
          Returns f (x), the density of X evaluated at x.
 double getMean()
          Returns the mean of the distribution function.
 int getN()
          Returns n, the number of observations.
 double getObs(int i)
          Returns the value of X(i).
 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 of the distribution function.
 double getVariance()
          Returns the variance of the distribution function.
 double inverseF(double u)
          Computes and returns the inverse distribution function F-1(u), defined in.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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
Computes and 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 interface: Distribution
Returns 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 interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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.


SSJ
V. 1.2.5.

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