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 occuring will be exactly x.
The POSSON 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.

where,

X - are represents number of events.

Mean - is the expected numeric values.

Cumulative - returned the logical value that determines the form of the probability distribution.

If TRUE - returnd the cumulative Poisson probability that the number of random events occuring will be between 0 and X.

If FALSE -returns the Poisson probability mass function that the number of events occuring will be exactly X.

Returns the Poisson distribution.

Formula :-

If Cumulative =FALSE

POISSON = (e^{-λ _λ× _{) / x!}}

If Cumulative = TRUE

POISSON = Σ(e^{-λ _λ×_{) /k!}}

If X orMean is nonnumeric, POISSON returns the #ERROR.

If X < 0 or Mean < 0 ,POISSON returns the #ERROR.

POISSON

Lets see an example in (Column1, Row1)

?UNIQ1bbe901cd2555324-nowiki-00000004-QINU?

POISSON returns 0.44568.

Cosider an another example

?UNIQ1bbe901cd2555324-nowiki-00000005-QINU?

POISSON returns 0.195367.

Syntax

Remarks

Examples

Description