Class PoissonDistribution
java.lang.Object
org.hipparchus.distribution.discrete.AbstractIntegerDistribution
org.hipparchus.distribution.discrete.PoissonDistribution
- All Implemented Interfaces:
Serializable
,IntegerDistribution
Implementation of the Poisson distribution.
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Field Summary
Modifier and TypeFieldDescriptionstatic final double
Default convergence criterion.static final int
Default maximum number of iterations for cumulative probability calculations. -
Constructor Summary
ConstructorDescriptionPoissonDistribution
(double p) Creates a new Poisson distribution with specified mean.PoissonDistribution
(double p, double epsilon) Creates a new Poisson distribution with the specified mean and convergence criterion.PoissonDistribution
(double p, double epsilon, int maxIterations) Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.PoissonDistribution
(double p, int maxIterations) Creates a new Poisson distribution with the specified mean and maximum number of iterations. -
Method Summary
Modifier and TypeMethodDescriptiondouble
cumulativeProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
getMean()
Get the mean for the distribution.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.int
Access the lower bound of the support.int
Access the upper bound of the support.boolean
Use this method to get information about whether the support is connected, i.e.double
logProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
is the natural logarithm.double
normalApproximateProbability
(int x) Calculates the Poisson distribution function using a normal approximation.double
probability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.Methods inherited from class org.hipparchus.distribution.discrete.AbstractIntegerDistribution
inverseCumulativeProbability, probability, solveInverseCumulativeProbability
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Field Details
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DEFAULT_MAX_ITERATIONS
public static final int DEFAULT_MAX_ITERATIONSDefault maximum number of iterations for cumulative probability calculations.- See Also:
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DEFAULT_EPSILON
public static final double DEFAULT_EPSILONDefault convergence criterion.- See Also:
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Constructor Details
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PoissonDistribution
Creates a new Poisson distribution with specified mean.- Parameters:
p
- the Poisson mean- Throws:
MathIllegalArgumentException
- ifp <= 0
.
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PoissonDistribution
public PoissonDistribution(double p, double epsilon, int maxIterations) throws MathIllegalArgumentException Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.- Parameters:
p
- Poisson mean.epsilon
- Convergence criterion for cumulative probabilities.maxIterations
- the maximum number of iterations for cumulative probabilities.- Throws:
MathIllegalArgumentException
- ifp <= 0
.
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PoissonDistribution
Creates a new Poisson distribution with the specified mean and convergence criterion.- Parameters:
p
- Poisson mean.epsilon
- Convergence criterion for cumulative probabilities.- Throws:
MathIllegalArgumentException
- ifp <= 0
.
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PoissonDistribution
public PoissonDistribution(double p, int maxIterations) Creates a new Poisson distribution with the specified mean and maximum number of iterations.- Parameters:
p
- Poisson mean.maxIterations
- Maximum number of iterations for cumulative probabilities.
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Method Details
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getMean
public double getMean()Get the mean for the distribution.- Returns:
- the mean for the distribution.
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probability
public double probability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(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
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logProbability
public double logProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
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 ofIntegerDistribution.probability(int)
.The default implementation simply computes the logarithm of
probability(x)
.- Specified by:
logProbability
in interfaceIntegerDistribution
- Overrides:
logProbability
in classAbstractIntegerDistribution
- Parameters:
x
- the point at which the PMF is evaluated- Returns:
- the logarithm of the value of the probability mass function at
x
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cumulativeProbability
public double cumulativeProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(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
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normalApproximateProbability
public double normalApproximateProbability(int x) Calculates the Poisson distribution function using a normal approximation. TheN(mean, sqrt(mean))
distribution is used to approximate the Poisson distribution. The computation uses "half-correction" (evaluating the normal distribution function atx + 0.5
).- Parameters:
x
- Upper bound, inclusive.- Returns:
- the distribution function value calculated using a normal approximation.
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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. For mean parameterp
, the mean isp
.- Returns:
- the mean or
Double.NaN
if it is not defined
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. For mean parameterp
, the variance isp
.- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
orDouble.NaN
if it is not defined)
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getSupportLowerBound
public int getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must return
The lower bound of the support is always 0 no matter the mean parameter.inf {x in Z | P(X <= x) > 0}
.- Returns:
- lower bound of the support (always 0)
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getSupportUpperBound
public int getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must return
The upper bound of the support is positive infinity, regardless of the parameter values. There is no integer infinity, so this method returnsinf {x in R | P(X <= x) = 1}
.Integer.MAX_VALUE
.- Returns:
- upper bound of the support (always
Integer.MAX_VALUE
for positive infinity)
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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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