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## org.apache.commons.math.distribution
Class PoissonDistributionImpl

    java.lang.Object
      org.apache.commons.math.distribution.AbstractDistribution
          org.apache.commons.math.distribution.AbstractIntegerDistribution
              org.apache.commons.math.distribution.PoissonDistributionImpl

All Implemented Interfaces:
  DiscreteDistribution, Distribution, IntegerDistribution, PoissonDistribution, Serializable

public class PoissonDistributionImpl
extends AbstractIntegerDistribution
implements PoissonDistribution, Serializable

Implementation for the `PoissonDistribution`.

Version:
  $Revision: 355770 $ $Date: 2005-12-10 12:48:57 -0700 (Sat, 10 Dec 2005) $
See Also:
  Serialized Form

Constructor Summary
`PoissonDistributionImpl(double p)` Create a new Poisson distribution with the given the mean.

Method Summary
`double` | `cumulativeProbability(int x)` The probability distribution function P(X <= x) for a Poisson distribution.
`protected int` | `getDomainLowerBound(double p)` Access the domain value lower bound, based on `p`, used to bracket a CDF root.
`protected int` | `getDomainUpperBound(double p)` Access the domain value upper bound, based on `p`, used to bracket a CDF root.
`double` | `getMean()` Get the Poisson mean 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.
`void` | `setMean(double p)` Set the Poisson mean for the distribution.

Methods inherited from class org.apache.commons.math.distribution.AbstractIntegerDistribution
`cumulativeProbability, cumulativeProbability, inverseCumulativeProbability, probability`

Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution
`cumulativeProbability`

Methods inherited from class java.lang.Object
`clone, equals, finalize, 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`

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:
  `IllegalArgumentException` - if p ≤ 0

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

    public void setMean(double p)

  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:
    `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

### getDomainLowerBound

    protected int getDomainLowerBound(double p)

  Access the domain value lower bound, based on `p`, used to bracket a CDF root. This method is used by `AbstractIntegerDistribution.inverseCumulativeProbability(double)` to find critical values.

  Specified by:
    `getDomainLowerBound` in class `AbstractIntegerDistribution`
  Parameters:
    `p` - the desired probability for the critical value
  Returns:
    domain lower bound

### getDomainUpperBound

    protected int getDomainUpperBound(double p)

  Access the domain value upper bound, based on `p`, used to bracket a CDF root. This method is used by `AbstractIntegerDistribution.inverseCumulativeProbability(double)` to find critical values.

  Specified by:
    `getDomainUpperBound` in class `AbstractIntegerDistribution`
  Parameters:
    `p` - the desired probability for the critical value
  Returns:
    domain upper bound

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