org.apache.commons.statistics.distribution

## Interface DiscreteDistribution

• ### Nested Class Summary

Nested Classes
Modifier and Type Interface and Description
static interface  DiscreteDistribution.Sampler
Sampling functionality.
• ### Method Summary

All Methods
Modifier and Type Method and Description
DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
double cumulativeProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double getMean()
Gets the mean of this distribution.
int getSupportLowerBound()
Gets the lower bound of the support.
int getSupportUpperBound()
Gets the upper bound of the support.
double getVariance()
Gets the variance of this distribution.
int inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
boolean isSupportConnected()
Indicates whether the support is connected, i.e.
default double logProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
double probability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double probability(int x0, int x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
• ### Method Detail

• #### logProbability

default double logProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
Parameters:
x - Point at which the PMF is evaluated.
Returns:
the logarithm of the value of the probability mass function at x.
• #### probability

double probability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.
Parameters:
x - Point at which the PMF is evaluated.
Returns:
the value of the probability mass function at x.
• #### probability

double probability(int x0,
int x1)
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
Parameters:
x0 - Lower bound (exclusive).
x1 - Upper bound (inclusive).
Returns:
the probability that a random variable with this distribution will take a value between x0 and x1, excluding the lower and including the upper endpoint.
Throws:
IllegalArgumentException - if x0 > x1.
• #### cumulativeProbability

double cumulativeProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other, words, this method represents the (cumulative) distribution function (CDF) for this distribution.
Parameters:
x - Point at which the CDF is evaluated.
Returns:
the probability that a random variable with this distribution takes a value less than or equal to x.
• #### inverseCumulativeProbability

int inverseCumulativeProbability(double p)
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
• inf{x in Z | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in Z | P(X<=x) > 0} for p = 0.
If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned.
Parameters:
p - Cumulative probability.
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
Throws:
IllegalArgumentException - if p < 0 or p > 1.
• #### getMean

double getMean()
Gets the mean of this distribution.
Returns:
the mean, or Double.NaN if it is not defined.
• #### getVariance

double getVariance()
Gets the variance of this distribution.
Returns:
the variance, or Double.NaN if it is not defined.
• #### getSupportLowerBound

int getSupportLowerBound()
Gets the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0), i.e. inf {x in Z | P(X <= x) > 0}. By convention, Integer.MIN_VALUE should be substituted for negative infinity.
Returns:
the lower bound of the support.
• #### getSupportUpperBound

int getSupportUpperBound()
Gets the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1), i.e. inf {x in R | P(X <= x) = 1}. By convention, Integer.MAX_VALUE should be substituted for positive infinity.
Returns:
the upper bound of the support.
• #### isSupportConnected

boolean isSupportConnected()
Indicates whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support.
Returns:
whether the support is connected.
• #### createSampler

DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.