PoissonDistribution (NMDEV 1.2.9 API)

java.lang.Object
- dev.nm.stat.distribution.univariate.PoissonDistribution

All Implemented Interfaces:

ProbabilityDistribution
```
public class PoissonDistribution
extends 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

Constructor Summary

Constructors
Constructor and Description

PoissonDistribution(double lambda)
Construct a Poisson distribution.

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

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`ccdf(double x)` The complementary cumulative distribution function.
`double`	`cdf(double k)` Gets 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()` Gets the entropy of this distribution.
`double`	`kurtosis()` Gets the excess kurtosis of this distribution.
`double`	`mean()` Gets the mean of this distribution.
`double`	`median()` Gets the median of this distribution.
`double`	`moment(double t)` The moment generating function is the expected value of \(e^{tX}\).
`double`	`quantile(double u)` Gets the quantile, the inverse of the cumulative distribution function.
`double`	`skew()` Gets the skewness of this distribution.
`double`	`variance()` Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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
    
    Gets 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. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] 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 - t
    
    Returns:
    
    E(exp(tX))
    
    See Also:
    
    Wikipedia: Moment-generating function

Class PoissonDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PoissonDistribution

Method Detail

mean

median

variance

skew

kurtosis

entropy

cdf

ccdf

density

quantile

moment