Difference between revisions of "Manuals/calci/poisson"
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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 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. | *If it is FALSE,this function will give the Poisson probability mass function with the number of events occurring will be exactly x. | ||
| − | *The <math>POISSON </math>probability mass function is: <math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>, <math>x=0,1,2,...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</math>>0. <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 | *This function will return the result as error when | ||
Revision as of 03:40, 7 January 2014
POISSON(x,m,cu)
- 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} is the number of events.
- 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 the mean
- 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 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 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 POISSON(x,m,cu), x } is the number of events in a given interval of time, 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 the Average numeric value and 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 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 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 POISSON } probability mass 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 x=0,1,2,...} where 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 \lambda } is the shape parameter and 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 \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
, 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=0,1,2,...}
where 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 \lambda }
is the shape parameter and 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 \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).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
- =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