org.apache.commons.math.distribution

Class PoissonDistributionImpl

• Field Summary

Fields
Modifier and Type Field and Description
`static double` `DEFAULT_EPSILON`
Default convergence criterion.
`static int` `DEFAULT_MAX_ITERATIONS`
Default maximum number of iterations for cumulative probability calculations.
• Constructor Summary

Constructors
Constructor and Description
`PoissonDistributionImpl(double p)`
Create a new Poisson distribution with the given the mean.
```PoissonDistributionImpl(double p, double epsilon)```
Create a new Poisson distribution with the given mean and convergence criterion.
```PoissonDistributionImpl(double p, double epsilon, int maxIterations)```
Create a new Poisson distribution with the given mean, convergence criterion and maximum number of iterations.
```PoissonDistributionImpl(double p, int maxIterations)```
Create a new Poisson distribution with the given mean and maximum number of iterations.
```PoissonDistributionImpl(double p, NormalDistribution z)```
Deprecated.
as of 2.1 (to avoid possibly inconsistent state, the "NormalDistribution" will be instantiated internally)
• Method Summary

All Methods
Modifier and Type Method and Description
`double` `cumulativeProbability(int x)`
The probability distribution function P(X <= x) for a Poisson distribution.
`double` `getMean()`
Get the Poisson mean for the distribution.
`double` `getNumericalVariance()`
Returns the variance of the distribution.
`int` `getSupportLowerBound()`
Returns the lower bound of the support for the distribution.
`int` `getSupportUpperBound()`
Returns the upper bound of the support for the distribution.
`double` `normalApproximateProbability(int x)`
Calculates the Poisson distribution function using a normal approximation.
`double` `probability(int x)`
The probability mass function P(X = x) for a Poisson distribution.
`int` `sample()`
Generates a random value sampled from this distribution.
`void` `setMean(double p)`
Deprecated.
as of 2.1 (class will become immutable in 3.0)
`void` `setNormal(NormalDistribution value)`
Deprecated.
as of 2.1 (class will become immutable in 3.0)
• Methods inherited from class org.apache.commons.math.distribution.AbstractIntegerDistribution

`cumulativeProbability, cumulativeProbability, cumulativeProbability, inverseCumulativeProbability, isSupportLowerBoundInclusive, isSupportUpperBoundInclusive, probability, reseedRandomGenerator, sample`
• Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• Methods inherited from interface org.apache.commons.math.distribution.IntegerDistribution

`cumulativeProbability, inverseCumulativeProbability`
• Methods inherited from interface org.apache.commons.math.distribution.DiscreteDistribution

`probability`
• Methods inherited from interface org.apache.commons.math.distribution.Distribution

`cumulativeProbability, cumulativeProbability`
• Field Detail

• DEFAULT_MAX_ITERATIONS

`public static final int DEFAULT_MAX_ITERATIONS`
Default maximum number of iterations for cumulative probability calculations.
Since:
2.1
Constant Field Values
• DEFAULT_EPSILON

`public static final double DEFAULT_EPSILON`
Default convergence criterion.
Since:
2.1
Constant Field Values
• Constructor Detail

• PoissonDistributionImpl

`public PoissonDistributionImpl(double p)`
Create a new Poisson distribution with the given the mean. The mean value must be positive; otherwise an `IllegalArgument` is thrown.
Parameters:
`p` - the Poisson mean
Throws:
`java.lang.IllegalArgumentException` - if p ≤ 0
• PoissonDistributionImpl

```public PoissonDistributionImpl(double p,
double epsilon,
int maxIterations)```
Create a new Poisson distribution with the given mean, convergence criterion and maximum number of iterations.
Parameters:
`p` - the Poisson mean
`epsilon` - the convergence criteria for cumulative probabilites
`maxIterations` - the maximum number of iterations for cumulative probabilites
Since:
2.1
• PoissonDistributionImpl

```public PoissonDistributionImpl(double p,
double epsilon)```
Create a new Poisson distribution with the given mean and convergence criterion.
Parameters:
`p` - the Poisson mean
`epsilon` - the convergence criteria for cumulative probabilites
Since:
2.1
• PoissonDistributionImpl

```public PoissonDistributionImpl(double p,
int maxIterations)```
Create a new Poisson distribution with the given mean and maximum number of iterations.
Parameters:
`p` - the Poisson mean
`maxIterations` - the maximum number of iterations for cumulative probabilites
Since:
2.1
• PoissonDistributionImpl

```@Deprecated
public PoissonDistributionImpl(double p,
NormalDistribution z)```
Deprecated. as of 2.1 (to avoid possibly inconsistent state, the "NormalDistribution" will be instantiated internally)
Create a new Poisson distribution with the given the mean. The mean value must be positive; otherwise an `IllegalArgument` is thrown.
Parameters:
`p` - the Poisson mean
`z` - a normal distribution used to compute normal approximations.
Throws:
`java.lang.IllegalArgumentException` - if p ≤ 0
Since:
1.2
• Method Detail

• getMean

`public double getMean()`
Get the Poisson mean for the distribution.
Specified by:
`getMean` in interface `PoissonDistribution`
Returns:
the Poisson mean for the distribution.
• setMean

```@Deprecated
public void setMean(double p)```
Deprecated. as of 2.1 (class will become immutable in 3.0)
Set the Poisson mean for the distribution. The mean value must be positive; otherwise an `IllegalArgument` is thrown.
Specified by:
`setMean` in interface `PoissonDistribution`
Parameters:
`p` - the Poisson mean value
Throws:
`java.lang.IllegalArgumentException` - if p ≤ 0
• probability

`public double probability(int x)`
The probability mass function P(X = x) for a Poisson distribution.
Specified by:
`probability` in interface `IntegerDistribution`
Parameters:
`x` - the value at which the probability density function is evaluated.
Returns:
the value of the probability mass function at x
• cumulativeProbability

```public double cumulativeProbability(int x)
throws MathException```
The probability distribution function P(X <= x) for a Poisson distribution.
Specified by:
`cumulativeProbability` in interface `IntegerDistribution`
Specified by:
`cumulativeProbability` in class `AbstractIntegerDistribution`
Parameters:
`x` - the value at which the PDF is evaluated.
Returns:
Poisson distribution function evaluated at x
Throws:
`MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.
• normalApproximateProbability

```public double normalApproximateProbability(int x)
throws MathException```
Calculates the Poisson distribution function using a normal approximation. The `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`

Specified by:
`normalApproximateProbability` in interface `PoissonDistribution`
Parameters:
`x` - the upper bound, inclusive
Returns:
the distribution function value calculated using a normal approximation
Throws:
`MathException` - if an error occurs computing the normal approximation
• sample

```public int sample()
throws MathException```
Generates a random value sampled from this distribution.

Algorithm Description:

• For small means, uses simulation of a Poisson process using Uniform deviates, as described here. The Poisson process (and hence value returned) is bounded by 1000 * mean.
• <
• For large means, uses the rejection algorithm described in
Devroye, Luc. (1981).The Computer Generation of Poisson Random Variables Computing vol. 26 pp. 197-207.

Overrides:
`sample` in class `AbstractIntegerDistribution`
Returns:
random value
Throws:
`MathException` - if an error occurs generating the random value
Since:
2.2
• setNormal

```@Deprecated
public void setNormal(NormalDistribution value)```
Deprecated. as of 2.1 (class will become immutable in 3.0)
Modify the normal distribution used to compute normal approximations. The caller is responsible for insuring the normal distribution has the proper parameter settings.
Parameters:
`value` - the new distribution
Since:
1.2
• getSupportLowerBound

`public int getSupportLowerBound()`
Returns the lower bound of the support for the distribution. The lower bound of the support is always 0 no matter the mean parameter.
Returns:
lower bound of the support (always 0)
Since:
2.2
• getSupportUpperBound

`public int getSupportUpperBound()`
Returns the upper bound of the support for the distribution. The upper bound of the support is positive infinity, regardless of the parameter values. There is no integer infinity, so this method returns `Integer.MAX_VALUE` and `AbstractIntegerDistribution.isSupportUpperBoundInclusive()` returns `true`.
Returns:
upper bound of the support (always `Integer.MAX_VALUE` for positive infinity)
Since:
2.2
• getNumericalVariance

`public double getNumericalVariance()`
Returns the variance of the distribution. For mean parameter `p`, the variance is `p`
Returns:
the variance
Since:
2.2