Manuals/calci/poisson

POISSON(x,m,cu)

• $x$ is the number of events.
• $m$ is the mean
• $cu$ 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 $POISSON(x,m,cu)$, $x$ 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 $\lambda >0$. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} is the base of the natural logarithm (e=2.718282).

• The Cumulative Poisson Probability function is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F(k,\lambda)=\sum_{k=0}^x \frac{e^{-\lambda} .\lambda^k}{k!}} .

• This function will return the result as error when

1.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m}
 is non-numeric.
2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x<0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m<0}
.

Examples

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

Related Videos

POISSON

See Also

• EXPONDIST

References

Poisson distribution