umontreal.iro.lecuyer.probdist
Class ContinuousEmpiricalDist

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

All Implemented Interfaces:

Distribution

public class ContinuousEmpiricalDist
extends ContinuousDistribution

Extends the ContinuousDistribution for the empirical distribution with known individual observations. Let X₁,..., X_n be the empirical observations and X₍₁₎,..., X_(n), the same observations sorted in increasing order. The empirical distribution has density

f (x) = 1/[(n - 1)(X_(I+1) - X_(I))] for X_(I) <= x < X_(I+1) where I = 1, 2,..., n - 1.

It has distribution function

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.

Its inverse function is given by

F^-1(u) = X_(I) + ((n - 1)u - I + 1)(X_(I+1) - X_(I)) for (I - 1)/(n - 1) <= u <= I/(n - 1),

where I = 1,..., n - 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

ContinuousEmpiricalDist(double[] obs)
Constructs a new empirical distribution using all the observations stored into obs.

ContinuousEmpiricalDist(InputStreamReader in)
Constructs a new empirical distribution using the observations read from the input stream 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.
int	getN() Returns n, the number of observations.
double	getObs(int i) Returns the value of X(i), the ith order observation.
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

ContinuousEmpiricalDist

public ContinuousEmpiricalDist(double[] obs)

Constructs a new empirical distribution using all the observations stored into obs. The given array obs will be modified by this method and should not be modified by the caller afterwards.

ContinuousEmpiricalDist

public ContinuousEmpiricalDist(InputStreamReader in)
                        throws IOException

Constructs a new empirical distribution using the observations read from the input stream reader in. The constructor will read the first double of each line in the stream. The format of the file is the same as in UNURAN. If a line does not start with +, - or a digit, it will be ignored. One must be careful about lines starting with a blank.

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), the ith order observation.

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.