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(InputStreamReader 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.
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	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(InputStreamReader in)
                             throws IOException

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

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.