org.apache.commons.statistics.distribution

## Interface DiscreteDistribution

• ### Nested Class Summary

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

All Methods
Modifier and Type Method and Description
DiscreteDistribution.Sampler createSampler(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.
default int inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution.
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).
default 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).
default double survivalProbability(int x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).
• ### Method Detail

• #### 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

default 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). The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Special cases:

• returns 0.0 if x0 == x1;
• returns probability(x1) if x0 + 1 == x1;
Parameters:
x0 - Lower bound (exclusive).
x1 - Upper bound (inclusive).
Returns:
the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.
Throws:
IllegalArgumentException - if x0 > x1.
• #### 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.
• #### 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.
• #### survivalProbability

default double survivalProbability(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 complementary cumulative distribution function.

By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

Parameters:
x - Point at which the survival function is evaluated.
Returns:
the probability that a random variable with this distribution takes a value greater than 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:

$x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases}$

If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of cumulativeProbability(x) called using the returned p-quantile may not compute the original p.

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.
• #### inverseSurvivalProbability

default int inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

$x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \ge x) \lt 1 \} & \text{for } p = 1 \end{cases}$

If the result exceeds the range of the data type int, then Integer.MIN_VALUE or Integer.MAX_VALUE is returned. In this case the result of survivalProbability(x) called using the returned (1-p)-quantile may not compute the original p.

By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

Parameters:
p - Cumulative probability.
Returns:
the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
Throws:
IllegalArgumentException - if p < 0 or p > 1.
• #### getMean

double getMean()
Gets the mean of this distribution.
Returns:
the mean.
• #### getVariance

double getVariance()
Gets the variance of this distribution.
Returns:
the variance.
• #### getSupportLowerBound

int getSupportLowerBound()
Gets the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0), i.e. $$\inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \}$$. 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. $$\inf \{ x \in \mathbb Z : P(X \le x) = 1 \}$$. By convention, Integer.MAX_VALUE should be substituted for positive infinity.
Returns:
the upper bound of the support.
• #### createSampler

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