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java.lang.Objectorg.apache.commons.math3.distribution.AbstractIntegerDistribution
org.apache.commons.math3.distribution.PoissonDistribution
public class PoissonDistribution
Implementation of the Poisson distribution.
| Field Summary | |
|---|---|
static double |
DEFAULT_EPSILON
Default convergence criterion. |
static int |
DEFAULT_MAX_ITERATIONS
Default maximum number of iterations for cumulative probability calculations. |
| Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution |
|---|
random, randomData |
| Constructor Summary | |
|---|---|
PoissonDistribution(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. |
|
PoissonDistribution(RandomGenerator rng,
double p,
double epsilon,
int maxIterations)
Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations. |
|
| Method Summary | |
|---|---|
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()
Get the mean for the distribution. |
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. |
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 |
normalApproximateProbability(int x)
Calculates the Poisson distribution function using a normal approximation. |
double |
probability(int x)
For a random variable X whose values are distributed according
to this distribution, this method returns P(X = x). |
int |
sample()
Generate a random value sampled from this distribution. |
| Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution |
|---|
cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, solveInverseCumulativeProbability |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
|---|
public static final int DEFAULT_MAX_ITERATIONS
public static final double DEFAULT_EPSILON
| Constructor Detail |
|---|
public PoissonDistribution(double p)
throws NotStrictlyPositiveException
p - the Poisson mean
NotStrictlyPositiveException - if p <= 0.
public PoissonDistribution(double p,
double epsilon,
int maxIterations)
throws NotStrictlyPositiveException
p - Poisson mean.epsilon - Convergence criterion for cumulative probabilities.maxIterations - the maximum number of iterations for cumulative
probabilities.
NotStrictlyPositiveException - if p <= 0.
public PoissonDistribution(RandomGenerator rng,
double p,
double epsilon,
int maxIterations)
throws NotStrictlyPositiveException
rng - Random number generator.p - Poisson mean.epsilon - Convergence criterion for cumulative probabilities.maxIterations - the maximum number of iterations for cumulative
probabilities.
NotStrictlyPositiveException - if p <= 0.
public PoissonDistribution(double p,
double epsilon)
throws NotStrictlyPositiveException
p - Poisson mean.epsilon - Convergence criterion for cumulative probabilities.
NotStrictlyPositiveException - if p <= 0.
public PoissonDistribution(double p,
int maxIterations)
p - Poisson mean.maxIterations - Maximum number of iterations for cumulative
probabilities.| Method Detail |
|---|
public double getMean()
public double probability(int x)
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.
x - the point at which the PMF is evaluated
xpublic double cumulativeProbability(int x)
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.
x - the point at which the CDF is evaluated
xpublic double normalApproximateProbability(int x)
N(mean, sqrt(mean)) distribution is used
to approximate the Poisson distribution. The computation uses
"half-correction" (evaluating the normal distribution function at
x + 0.5).
x - Upper bound, inclusive.
public double getNumericalMean()
p, the mean is p.
Double.NaN if it is not definedpublic double getNumericalVariance()
p, the variance is p.
Double.POSITIVE_INFINITY or
Double.NaN if it is not defined)public int getSupportLowerBound()
inverseCumulativeProbability(0). In other words, this
method must return
inf {x in Z | P(X <= x) > 0}.
public int getSupportUpperBound()
inverseCumulativeProbability(1). In other words, this
method must return
inf {x in R | P(X <= x) = 1}.
Integer.MAX_VALUE.
Integer.MAX_VALUE for
positive infinity)public boolean isSupportConnected()
truepublic int sample()
Algorithm Description:
Devroye, Luc. (1981).The Computer Generation of Poisson Random Variables Computing vol. 26 pp. 197-207.
sample in interface IntegerDistributionsample in class AbstractIntegerDistribution
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