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## cern.jet.random
Class Poisson

    java.lang.Object
      cern.colt.PersistentObject
          cern.jet.random.AbstractDistribution
              cern.jet.random.AbstractDiscreteDistribution
                  cern.jet.random.Poisson

All Implemented Interfaces:
  Cloneable, DoubleFunction, IntFunction, Serializable

public class Poisson
extends AbstractDiscreteDistribution

Poisson distribution (quick); See the math definition and animated definition.

`p(k) = (mean^k / k!) * exp(-mean)` for `k >= 0`.

Valid parameter ranges: `mean > 0`. Note: if `mean <= 0.0` then always returns zero.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation: High performance implementation. Patchwork Rejection/Inversion method.

This is a port of `pprsc.c` from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

H. Zechner (1994): Efficient sampling from continuous and discrete unimodal distributions, Doctoral Dissertation, 156 pp., Technical University Graz, Austria.

Also see

Stadlober E., H. Zechner (1999), The patchwork rejection method for sampling from unimodal distributions, to appear in ACM Transactions on Modelling and Simulation.

Version:
  1.0, 09/24/99
See Also:
  Serialized Form

Field Summary

Fields inherited from class cern.colt.PersistentObject
`serialVersionUID`

Constructor Summary
`Poisson(double mean, RandomEngine randomGenerator)` Constructs a poisson distribution.

Method Summary
`double` | `cdf(int k)` Returns the cumulative distribution function.
`Object` | `clone()` Returns a deep copy of the receiver; the copy will produce identical sequences.
`int` | `nextInt()` Returns a random number from the distribution.
`int` | `nextInt(double theMean)` Returns a random number from the distribution; bypasses the internal state.
`double` | `pdf(int k)` Returns the probability distribution function.
`void` | `setMean(double mean)` Sets the mean.
`static int` | `staticNextInt(double mean)` Returns a random number from the distribution with the given mean.
`String` | `toString()` Returns a String representation of the receiver.

Methods inherited from class cern.jet.random.AbstractDiscreteDistribution
`nextDouble`

Methods inherited from class cern.jet.random.AbstractDistribution
`apply, apply, makeDefaultGenerator`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### Poisson

    public Poisson(double mean,
                   RandomEngine randomGenerator)

  Constructs a poisson distribution. Example: mean=1.0.

Method Detail

### cdf

    public double cdf(int k)

  Returns the cumulative distribution function.

### clone

    public Object clone()

  Returns a deep copy of the receiver; the copy will produce identical sequences. After this call has returned, the copy and the receiver have equal but separate state.

  Overrides:
    `clone` in class `AbstractDistribution`
  Returns:
    a copy of the receiver.

### nextInt

    public int nextInt()

  Returns a random number from the distribution.

  Specified by:
    `nextInt` in class `AbstractDiscreteDistribution`

### nextInt

    public int nextInt(double theMean)

  Returns a random number from the distribution; bypasses the internal state.

### pdf

    public double pdf(int k)

  Returns the probability distribution function.

### setMean

    public void setMean(double mean)

  Sets the mean.

### staticNextInt

    public static int staticNextInt(double mean)

  Returns a random number from the distribution with the given mean.

### toString

    public String toString()

  Returns a String representation of the receiver.

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