Difference between revisions of "Manuals/calci/poisson"

Revision as of 03:12, 22 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 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:

$F(k,\lambda )=\sum _{k=0}^{x}{\frac {e^{-\lambda }.\lambda ^{k}}{k!}}$ .

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

@@ Line 11: / Line 11: @@
 *If it is TRUE, this function will give the Cumulative Poisson Probability with the number of random events between <math>0</math> and <math>x</math>(included).
 *If it is FALSE, this function will give the Poisson Probability Mass function with the number of events occurring will be exactly <math>x</math>.
-*The <math>POISSON</math>probability mass function is: <math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>, <math>x=0,1,2,...</math>where <math> \lambda </math> is the shape parameter and <math>\lambda</math>>0. <math>e</math> 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>, <math>x=0,1,2,...</math>where <math> \lambda </math> is the shape parameter and <math>\lambda > 0</math>. <math>e</math> 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>.
+*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
 .<math>x</math> or <math>m</math> is non-numeric.