Poisson distribution
Story
The number \(n\) of arrivals of a Poisson process in unit time is Poisson distributed.
Example
The number of mutations in a strand of DNA per unit length (since mutations are rare) are Poisson distributed.
Parameters
The single parameter is the rate \(\lambda\) of the arrival of the Poisson process.
Support
The Poisson distribution is supported on the set of nonnegative integers.
Probability mass function
\[\begin{align}
f(n;\lambda) = \frac{\lambda^n}{n!}\,\mathrm{e}^{\lambda}.
\end{align}\]
Moments
Mean: \(\lambda\)
Variance: \(\lambda\)
Usage
Package 
Syntax 

NumPy 

SciPy 

Stan 
