Difference between revisions of "Manuals/calci/poisson"

Revision as of 03:31, 6 January 2014

POISSON(x,m,cu)

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 occuring 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 nonnumeric.
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

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 *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 occuring will be exactly x.
-*The <math>POISSON </math>probability mass function is: <math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>, x=0,1,2,...where <math> \lambda </math>is the shape parameter and <math>\lambda</math>>0.e is the base of the natural logarithm (e=2.718282).
+*The <math>POISSON </math>probability mass function is: <math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>,      x=0,1,2,...where <math> \lambda </math> is the shape parameter and <math>\lambda</math>>0. e is the base of the natural logarithm (e=2.718282).
 *The cumulative Poisson probability  function is:<math>F(k,\lambda)=\sum_{k=0}^x \frac{e^{-\lambda} .\lambda^k}{k!}</math>.
 *This function will return the result as error when