Manuals/calci/POISSON

POISSON(X,Lambda,Cumulative)

• $x$ is the number of events.
• $Lambda$ is the mean
• $Cumulative$ is the logical value like TRUE or FALSE.

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 $POISSON(X,Lambda,Cumulative)$, $X$ is the number of events in a given interval of time, $Lambda$ is the Average Numeric value and $Cumulative$ 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 $Lamda$ is non-numeric.
2.$X<0$ or $Lamda<0$.

Examples

1. POISSON(10,3,TRUE) = 0.9997076630493528
2. POISSON(10,3,FALSE) = 0.0008101511794681433
3. POISSON(21.7,7.54,TRUE) = 0.9999955033358848
4. POISSON(21.7,7.54,FALSE) = 0.00000948031184308478

See Also

• EXPONDIST

References

Poisson distribution

• List of Main Z Functions

• Z3 home