Manuals/calci/poisson

POISSON(x,m,cu)

Description

This function gives the value of the Poisson distribution.
The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time.
It is is used to model the number of events occurring within a given time interval.
In $POISSON(x,m,cu),x$ is the number of events in a given interval of time, $m$ is the Average numeric value and $cu$ is the logical value.
If it is TRUE, this function will give the cumulative Poisson probability with the number of random events between 0 and x(included).
If it is FALSE,this function will give the Poisson probability mass function with the number of events occurring will be exactly x.
The $POISSON$ probability mass function is: $f(x,\lambda )={\frac {\lambda ^{x}.e^{-\lambda }}{x!}}$ , $x=0,1,2,...$ where $\lambda$ is the shape parameter and $\lambda$ >0. $e$ is the base of the natural logarithm (e=2.718282).
The cumulative Poisson probability function is: $F(k,\lambda )=\sum _{k=0}^{x}{\frac {e^{-\lambda }.\lambda ^{k}}{k!}}$ .
This function will return the result as error when

1. $x$  or  $m$  is non-numeric.
2. $x<0$  or  $m<0$ .

=POISSON(6,2,TRUE) = 0.995466194
=POISSON(6,2,FALSE) = 0.012029803
=POISSON(10.2,7,TRUE) = 0.901479206
=POISSON(10.2,7,FALSE) = 0.070983269
=POISSON(6,0,TRUE) = 1