umontreal.iro.lecuyer.probdist
Class DiscreteDistribution

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

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ConstantDist, EmpiricalDist

public class DiscreteDistribution
extends Object
implements Distribution

This class implements discrete distributions over a finite set of real numbers (also over integers as a particular case). We assume that the random variable X of interest can take one of the n values x₀ < ^... < x_n-1, which must be sorted by increasing order. X can take the value x_k with probability p_k = P[X = x_k]. In addition to the methods specified in the interface Distribution, a method that returns the probability p_k is supplied.

Constructor Summary

DiscreteDistribution(double[] params)
Deprecated.

DiscreteDistribution(double[] values, double[] prob, int n)
Constructs a discrete distribution over the n values contained in array values, with probabilities given in array prob.

DiscreteDistribution(int[] values, double[] prob, int n)
Similar to DiscreteDistribution(double[], double[], int).

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
double	cdf(double x) Returns the distribution function F(x).
double	getMean() Computes the mean E[X] = ∑ipixi of the distribution.
int	getN() Returns the number of possible values xi.
double[]	getParams() Returns a table containing the parameters of the current distribution.
double	getStandardDeviation() Computes the standard deviation of the distribution.
double	getValue(int i) Returns the i-th value xi, for 0 <= i < n.
double	getVariance() Computes the variance Var[X] = ∑ipi(xi - E[X])2 of the distribution.
double	getXinf() Returns the lower limit x0 of the support of the distribution.
double	getXsup() Returns the upper limit xn-1 of the support 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 java.lang.Object

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

Constructor Detail

DiscreteDistribution

public DiscreteDistribution(double[] values,
                            double[] prob,
                            int n)

Constructs a discrete distribution over the n values contained in array values, with probabilities given in array prob. Both arrays must have at least n elements, the probabilities must sum to 1, and the values are assumed to be sorted by increasing order.

DiscreteDistribution

public DiscreteDistribution(int[] values,
                            double[] prob,
                            int n)

Similar to DiscreteDistribution(double[], double[], int).

DiscreteDistribution

@Deprecated
public DiscreteDistribution(double[] params)

Deprecated.

Constructs a discrete distribution whose parameters are given in a single ordered array: params[0] contains n, the number of values to consider. Then the next n values of params are the values x_j, and the last n values of params are the probabilities p_j.

Method Detail

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Specified by:

cdf in interface Distribution

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

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

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()

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

Specified by:

getMean in interface Distribution

getVariance

public double getVariance()

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

Specified by:

getVariance in interface Distribution

getStandardDeviation

public double getStandardDeviation()

Computes the standard deviation of the distribution.

Specified by:

getStandardDeviation in interface Distribution

getParams

public double[] getParams()

Returns a table containing the parameters of the current distribution. This table is built in regular order, according to constructor DiscreteDistribution(double[] params) order.

Specified by:

getParams in interface Distribution

getN

public int getN()

Returns the number of possible values x_i.

prob

public double prob(int i)

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

Parameters:

i - value number, 0 <= i < n

Returns:

the probability of value i

getValue

public double getValue(int i)

Returns the i-th value x_i, for 0 <= i < n.

getXinf

public double getXinf()

Returns the lower limit x₀ of the support of the distribution.

Returns:

x lower limit of support

getXsup

public double getXsup()

Returns the upper limit x_n-1 of the support of the distribution.

Returns:

x upper limit of support

toString

public String toString()

Returns a String containing information about the current distribution.

Overrides:

toString in class Object