com.numericalmethod.suanshu.stats.distribution.univariate

Class PoissonDistribution

java.lang.Object

com.numericalmethod.suanshu.stats.distribution.univariate.PoissonDistribution

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable

public class PoissonDistribution
extends java.lang.Object
implements ProbabilityDistribution

The Poisson distribution (or Poisson law of small numbers) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.

The R equivalent functions are dpois, ppois, qpois, rpois.

See Also:

• Wikipedia: Poisson distribution
• Wikipedia: Understanding Quantiles of Discrete Distributions

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
PoissonDistribution(double lambda) Construct a Poisson distribution.

Method Summary

Modifier and Type	Method and Description
double	ccdf(double x) The complementary cumulative distribution function.
double	cdf(double k) Get the cumulative probability F(x) = Pr(X ≤ x).
double	density(double k) The density function, which, if exists, is the derivative of F.
double	entropy() Get the entropy of this distribution.
double	kurtosis() Get the excess kurtosis of this distribution.
double	mean() Get the mean of this distribution.
double	median() Get the median of this distribution.
double	moment(double t) The moment generating function is the expected value of etX.
double	quantile(double u) Get the quantile, the inverse of the cumulative distribution function.
double	skew() Get the skewness of this distribution.
double	variance() Get the variance of this distribution.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PoissonDistribution

public PoissonDistribution(double lambda)

Construct a Poisson distribution.

Parameters:

lambda - the rate per interval

Method Detail

mean

public double mean()

Description copied from interface: ProbabilityDistribution

Get the mean of this distribution.

Specified by:

mean in interface ProbabilityDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

public double median()

Description copied from interface: ProbabilityDistribution

Get the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

public double variance()

Description copied from interface: ProbabilityDistribution

Get the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

public double skew()

Description copied from interface: ProbabilityDistribution

Get the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Description copied from interface: ProbabilityDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface ProbabilityDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

public double entropy()

Description copied from interface: ProbabilityDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface ProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double k)

Description copied from interface: ProbabilityDistribution

Get the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

k - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

ccdf

public double ccdf(double x)

The complementary cumulative distribution function.

Parameters:

x - x

Returns:

1 - F(x) = 1 - Pr(X ≤ x)

density

public double density(double k)

Description copied from interface: ProbabilityDistribution

The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.

f(x) = dF(X) / dx

This may not always exist.

For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.

Specified by:

density in interface ProbabilityDistribution

Parameters:

k - x

Returns:

f(x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

quantile

public double quantile(double u)

Description copied from interface: ProbabilityDistribution

Get the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.

 F-1(u) = x, such that
 Pr(X ≤ x) = u
 

This may not always exist.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - u, a quantile

Returns:

F^-1(u)

See Also:

Wikipedia: Quantile function

moment

public double moment(double t)

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of e^tX. That is,

E(e^tX)

This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

t - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function