umontreal.iro.lecuyer.probdist
Class PiecewiseLinearEmpiricalDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      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