org.apache.commons.math3.distribution

## Class GeometricDistribution

- java.lang.Object
- org.apache.commons.math3.distribution.AbstractIntegerDistribution
- org.apache.commons.math3.distribution.GeometricDistribution

- All Implemented Interfaces:
- Serializable, IntegerDistribution

public class GeometricDistributionextends AbstractIntegerDistribution

Implementation of the geometric distribution.

### Constructor Summary

Constructors Constructor and Description **GeometricDistribution**(double p)Create a geometric distribution with the given probability of success.**GeometricDistribution**(RandomGenerator rng, double p)Creates a geometric distribution.

### Method Summary

Methods Modifier and Type Method and Description `double`

**cumulativeProbability**(int x)For a random variable`X`

whose values are distributed according to this distribution, this method returns`P(X <= x)`

.`double`

**getNumericalMean**()Use this method to get the numerical value of the mean of this distribution.`double`

**getNumericalVariance**()Use this method to get the numerical value of the variance of this distribution.`double`

**getProbabilityOfSuccess**()Access the probability of success for this distribution.`int`

**getSupportLowerBound**()Access the lower bound of the support.`int`

**getSupportUpperBound**()Access the upper bound of the support.`boolean`

**isSupportConnected**()Use this method to get information about whether the support is connected, i.e.`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)`

.### Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

`cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample`

### Constructor Detail

#### GeometricDistribution

public GeometricDistribution(double p)

Create a geometric distribution with the given probability of success.- Parameters:
`p`

- probability of success.- Throws:
`OutOfRangeException`

- if`p <= 0`

or`p > 1`

.

#### GeometricDistribution

public GeometricDistribution(RandomGenerator rng, double p)

Creates a geometric distribution.- Parameters:
`rng`

- Random number generator.`p`

- Probability of success.- Throws:
`OutOfRangeException`

- if`p <= 0`

or`p > 1`

.

### Method Detail

#### getProbabilityOfSuccess

public double getProbabilityOfSuccess()

Access the probability of success for this distribution.- Returns:
- the probability of success.

#### probability

public 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`

- the point at which the PMF is evaluated- Returns:
- the value of the probability mass function at
`x`

#### logProbability

public 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. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of`IntegerDistribution.probability(int)`

.The default implementation simply computes the logarithm of

`probability(x)`

.**Overrides:**`logProbability`

in class`AbstractIntegerDistribution`

- Parameters:
`x`

- the point at which the PMF is evaluated- Returns:
- the logarithm of the value of the probability mass function at
`x`

#### cumulativeProbability

public 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`

- the 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`

#### getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For probability parameter`p`

, the mean is`(1 - p) / p`

.- Returns:
- the mean or
`Double.NaN`

if it is not defined

#### getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For probability parameter`p`

, the variance is`(1 - p) / (p * p)`

.- Returns:
- the variance (possibly
`Double.POSITIVE_INFINITY`

or`Double.NaN`

if it is not defined)

#### getSupportLowerBound

public int getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as`inverseCumulativeProbability(0)`

. In other words, this method must return

The lower bound of the support is always 0.`inf {x in Z | P(X <= x) > 0}`

.- Returns:
- lower bound of the support (always 0)

#### getSupportUpperBound

public int getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as`inverseCumulativeProbability(1)`

. In other words, this method must return

The upper bound of the support is infinite (which we approximate as`inf {x in R | P(X <= x) = 1}`

.`Integer.MAX_VALUE`

).- Returns:
- upper bound of the support (always Integer.MAX_VALUE)

#### isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.- Returns:
`true`

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