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 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

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

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	inverseF(double u) Computes and 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.

Methods inherited from class java.lang.Object

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

Constructor Detail

DiscreteDistribution

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

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.

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

Computes and returns the distribution function F(x).

Specified by:

cdf in interface Distribution

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

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the 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

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x