PHP Class MathPHP\Probability\Distribution\Discrete\Poisson

Inheritance: extends Discrete
Mostra file Open project: markrogoyski/math-php

Public Methods

Method Description
CDF ( integer $k, float $λ ) : float Cumulative Poisson Probability (lower culmulative distribution) - CDF The probability that the Poisson random variable is greater than some specified lower limit, and less than some specified upper limit.
PMF ( integer $k, float $λ ) : float Poisson distribution - probability mass function 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.

Method Details

CDF() public static method

k λˣℯ^⁻λ P(k,λ) = ∑ ------ ₓ₌₀ xᵢ!
public static CDF ( integer $k, float $λ ) : float
$k integer events in the interval
$λ float average number of successful events per interval
return float The cumulative Poisson probability

PMF() public static method

https://en.wikipedia.org/wiki/Poisson_distribution λᵏℯ^⁻λ P(k events in an interval) = ------ k!
public static PMF ( integer $k, float $λ ) : float
$k integer events in the interval
$λ float average number of successful events per interval
return float The Poisson probability of observing k successful events in an interval