public abstract class PoissonDistribution extends AbstractDiscreteDistribution
PoissonDistributionabstract class is used for calculating Poisson distributions. Poisson distributions are limits of Poisson processes, and are used to model rates of occurrences of events within a fixed period (of time, space, etc.). Poisson distributions are good models of lengths of texts or the rate of occurrence of words in text, as well as many other natural phenomena.
The Poisson distribution is a parametric discrete distribution
with a single parameter
λ > 0 which is the
average rate of occurrence of events in a period. The resulting
distribution provides a likelihood for each non-negative number of
outcomes. Specifically, the Poisson distribution with rate
parameter λ is defined for
k > 0 by:
Note that this definition produces a properly normalized probability distribution over natural numbers; if
Poissonλ(k) = e-λ λk / k!
λ > 0, then:
The expected value of a Poisson distribution is equal to the rate parameter:
Σk >= 0 Poissonλ(k) = 1.0
The variance is also equal to the rate parameter:
E(Poissonλ) = λ
Var(Poissonλ) =def E([Poissonλ - E(Poissonλ)]2) = λ
Concrete subclasses need only implement the abstract
mean() method; the method
log2Probability(long) computes the
log (base 2) of the Poisson probability estimate for a given number
of outcomes in terms of the value of the rate parameter
lambda(). Logarithms are used to prevent over- and
underflow in calculations.
For more information, see:
|Modifier||Constructor and Description|
Construct an abstract Poisson distribution.
|Modifier and Type||Method and Description|
Returns the log (base 2) probability estimate in this Poisson distribution for the specified outcome.
Returns the mean of this Poisson distribution, which is equal to the rate parameter λ.
Returns the minimum outcome with non-zero probability,
Returns the probability estimate in this Poisson distribution for the specified outcome.
Returns the variance of this Poisson distribution, which is equal to the mean.
cumulativeProbability, cumulativeProbabilityGreater, cumulativeProbabilityLess, entropy, maxOutcome
public abstract double mean()
public double variance()
public long minOutcome()
public final double log2Probability(long outcome)
outcome- The outcome being estimated.
IllegalStateException- if the mean is not a positive finite value.
public final double probability(long outcome)
outcome- The outcome whose probability is returned.
IllegalStateException- If the mean is not a positive finite value.