umontreal.iro.lecuyer.probdist

Class DiscreteDistribution

java.lang.Object

umontreal.iro.lecuyer.probdist.DiscreteDistribution

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

EmpiricalDist

public class DiscreteDistribution
extends java.lang.Object
implements Distribution

Classes implementing discrete distributions over a finite set of real numbers should inherit from this class. For discrete distributions over integers, see DiscreteDistributionInt.

We assume that the random variable X of interest can take one of the n values x₀ < ^... < x_n-1 (which are sorted by increasing order). It takes 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.

Note that the default implementation of the complementary distribution function returns 1.0 - cdf(x - 1), which is not accurate when F(x) is near 1.

Constructor Summary

Constructors

Constructor and Description
DiscreteDistribution(double[] params) Constructs a discrete distribution whose parameters are given in a single ordered array: params[0] contains n, the number of values to consider.
DiscreteDistribution(double[] obs, double[] prob, int n) Constructs a discrete distribution over the n values contained in array obs, with probabilities given in array prob.

Method Summary

Modifier and Type	Method and Description
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] = ∑i=1npixi of the distribution.
double[]	getParams() Returns a table containing the parameters of the current distribution.
double	getStandardDeviation() Computes the standard deviation of the distribution.
double	getVariance() Computes the variance Var[X] = ∑i=1npi(xi - E[X])2 of the distribution.
double	getXinf() Returns the lower limit xa of the support of the distribution.
double	getXsup() Returns the upper limit xb of the support of the distribution.
double	inverseF(double u) Returns the inverse distribution function F-1(u), defined in.
double	prob(int k) Returns pk, the probability of the k-th observation, for 0 <= k < n.
java.lang.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[] obs,
                            double[] prob,
                            int n)

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

DiscreteDistribution

public DiscreteDistribution(double[] params)

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 observation values, and the last n values of params are the probabilities values.

Method Detail

prob

public double prob(int k)

Returns p_k, the probability of the k-th observation, for 0 <= k < n. The result should be a real number in the interval [0, 1].

Parameters:

k - observation number, 0 <= k < n

Returns:

the probability of observation k

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 must be 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 must be 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] = ∑_i=1ⁿp_ix_i of the distribution.

Specified by:

getMean in interface Distribution

getVariance

public double getVariance()

Computes the variance Var[X] = ∑_i=1ⁿp_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

getXinf

public double getXinf()

Returns the lower limit x_a of the support of the distribution. The probability is 0 for all x < x_a.

Returns:

x lower limit of support

getXsup

public double getXsup()

Returns the upper limit x_b of the support of the distribution. The probability is 0 for all x > x_b.

Returns:

x upper limit of support

toString

public java.lang.String toString()

Returns a String containing information about the current distribution.

Overrides:

toString in class java.lang.Object