Package org.hipparchus.distribution.discrete

Class GeometricDistribution

java.lang.Object

org.hipparchus.distribution.discrete.AbstractIntegerDistribution

org.hipparchus.distribution.discrete.GeometricDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

public class GeometricDistribution
extends AbstractIntegerDistribution

Implementation of the geometric distribution.

See Also:

Geometric distribution (Wikipedia), Geometric Distribution (MathWorld), Serialized Form

Constructor Summary

Constructors

Constructor	Description
GeometricDistribution(double p)	Create a geometric distribution with the given probability of success.

Method Summary

Modifier and Type	Method	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.
int	inverseCumulativeProbability(double p)	Computes the quantile function of this distribution.
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.hipparchus.distribution.discrete.AbstractIntegerDistribution

probability, solveInverseCumulativeProbability

Methods inherited from class java.lang.Object

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

Constructor Detail

GeometricDistribution

public GeometricDistribution(double p)
                      throws MathIllegalArgumentException

Create a geometric distribution with the given probability of success.

Parameters:

p - probability of success.

Throws:

MathIllegalArgumentException - 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).

Specified by:

logProbability in interface IntegerDistribution

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

inf {x in Z | P(X <= x) > 0}.

The lower bound of the support is always 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

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is infinite (which we approximate as 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

inverseCumulativeProbability

public int inverseCumulativeProbability(double p)
                                 throws MathIllegalArgumentException

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. The default implementation returns

• IntegerDistribution.getSupportLowerBound() for p = 0,
• IntegerDistribution.getSupportUpperBound() for p = 1, and
• AbstractIntegerDistribution.solveInverseCumulativeProbability(double, int, int) for 0 < p < 1.

Specified by:

inverseCumulativeProbability in interface IntegerDistribution

Overrides:

inverseCumulativeProbability in class AbstractIntegerDistribution

Parameters:

p - the cumulative probability

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Throws:

MathIllegalArgumentException - if p < 0 or p > 1