umontreal.iro.lecuyer.probdist
Class EmpiricalDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.DiscreteDistribution
      umontreal.iro.lecuyer.probdist.EmpiricalDist

All Implemented Interfaces:

Distribution

public class EmpiricalDist
extends DiscreteDistribution

Extends DiscreteDistribution to an empirical distribution function, based on the observations X₍₁₎,..., X_(n) (sorted by increasing order). The distribution is uniform over the n observations, so the distribution function has a jump of 1/n at each of the n observations.

Constructor Summary

EmpiricalDist(double[] obs)
Constructs a new empirical distribution using all the observations stored in obs, and which are assumed to have been sorted in increasing numerical order.

EmpiricalDist(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) Returns the distribution function F(x).
double	getInterQuartileRange() Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.
double	getMean() Computes the mean E[X] = ∑ipixi of the distribution.
double	getMedian() Returns the median.
static double	getMedian(double[] obs, int n) Returns the median.
int	getN() Returns n, the number of observations.
double	getObs(int i) Returns the value of X(i), for i = 0, 1,…, n - 1.
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() Computes the standard deviation of the distribution.
double	getVariance() Computes the variance Var[X] = ∑ipi(xi - E[X])2 of the distribution.
double	inverseF(double u) Returns the inverse distribution function F-1(u), defined in.
double	prob(int i) Returns pi, the probability of the i-th value, for 0 <= i < n.
String	toString() Returns a String containing information about the current distribution.

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistribution

getValue, getXinf, getXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

EmpiricalDist

public EmpiricalDist(double[] obs)

Constructs a new empirical distribution using all the observations stored in obs, and which are assumed to have been sorted in increasing numerical order. ¹ These observations are copied into an internal array.

EmpiricalDist

public EmpiricalDist(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. One must be careful about lines starting with a blank. This format is the same as in UNURAN. The observations read are assumed to have been sorted in increasing numerical order.

Throws:

IOException

Method Detail

prob

public double prob(int i)

Description copied from class: DiscreteDistribution

Returns p_i, the probability of the i-th value, for 0 <= i < n.

Overrides:

prob in class DiscreteDistribution

Parameters:

i - value number, 0 <= i < n

Returns:

the probability of value i

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class DiscreteDistribution

Parameters:

x - value at which the distribution function is evaluated

Returns:

the 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 DiscreteDistribution

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

the complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from interface: Distribution

Returns the inverse distribution function F^-1(u), defined in.

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class DiscreteDistribution

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 class: DiscreteDistribution

Computes the mean E[X] = ∑_ip_ix_i of the distribution.

Specified by:

getMean in interface Distribution

Overrides:

getMean in class DiscreteDistribution

getStandardDeviation

public double getStandardDeviation()

Description copied from class: DiscreteDistribution

Computes the standard deviation of the distribution.

Specified by:

getStandardDeviation in interface Distribution

Overrides:

getStandardDeviation in class DiscreteDistribution

getVariance

public double getVariance()

Description copied from class: DiscreteDistribution

Computes the variance Var[X] = ∑_ip_i(x_i - E[X])² of the distribution.

Specified by:

getVariance in interface Distribution

Overrides:

getVariance in class DiscreteDistribution

getMedian

public double getMedian()

Returns the median. Returns the n/2^th item of the sorted observations when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even.

getMedian

public static double getMedian(double[] obs,
                               int n)

Returns the median. Returns the n/2^th item of the array obs when the number of items is odd, and the mean of the n/2^th and the (n/2 + 1)^th items when the number of items is even. The array does not have to be sorted.

Parameters:

obs - the array of observations

n - the number of observations

Returns:

return the median of the observations

getN

public int getN()

Returns n, the number of observations.

Overrides:

getN in class DiscreteDistribution

getObs

public double getObs(int i)

Returns the value of X_(i), for i = 0, 1,…, n - 1.

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.

getInterQuartileRange

public double getInterQuartileRange()

Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.

getParams

public double[] getParams()

Return a table containing parameters of the current distribution.

Specified by:

getParams in interface Distribution

Overrides:

getParams in class DiscreteDistribution

toString

public String toString()

Returns a String containing information about the current distribution.

Overrides:

toString in class DiscreteDistribution