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Difference between revisions of "Manuals/calci/poisson"
 
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*<math>m </math> is the mean  
 
*<math>m </math> is the mean  
 
*<math>cu</math> is the logical value like TRUE or FALSE.
 
*<math>cu</math> is the logical value like TRUE or FALSE.
−
 
  
 
==Description==
 
==Description==
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*The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time.
 
*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.  
 
*It is  is used to model the number of events occurring within a given time interval.  
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*In <math>POISSON(x,m,cu), x </math> is the number of events in a given interval of time, <math> m </math> is the Average numeric value and <math> cu </math> is the logical value.  
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*In <math>POISSON(x,m,cu)</math>, <math>x</math> is the number of events in a given interval of time, <math>m </math> is the Average Numeric value and <math>cu</math> is the logical value.  
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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).
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*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).
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*If it is FALSE,this function will give the Poisson probability mass function with the number of events occuring will be exactly x.
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*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>.
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*The <math>POISSON </math>probability mass function is: <math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>, x=0,1,2,...where <math> \lambda </math>is the shape parameter and <math>\lambda</math>>0.e is the base of the natural logarithm (e=2.718282).
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*The <math>POISSON</math>probability mass function is:
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*The cumulative Poisson probability function is:<math>F(k,\lambda)=\sum_{k=0}^x \frac{e^{-\lambda} .\lambda^k}{k!}</math>.  
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<math> f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}</math>  
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<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:
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<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  
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  1.x or m is nonnumeric.
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  1.<math>x</math> or <math>m</math> is non-numeric.
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  2.x<0 or m<0.
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  2.<math>x<0</math> or <math>m<0</math>.
  
 
==Examples==
 
==Examples==
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#POISSON(6,2,TRUE)=0.995466194
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#=POISSON(6,2,TRUE) = 0.995466194
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#POISSON(6,2,FALSE)=0.012029803
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#=POISSON(6,2,FALSE) = 0.012029803
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#POISSON(10.2,7,TRUE)=0.901479206
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#=POISSON(10.2,7,TRUE) = 0.901479206
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#POISSON(10.2,7,FALSE)=0.070983269
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#=POISSON(10.2,7,FALSE) = 0.070983269
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#POISSON(6,0,TRUE)=1
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#=POISSON(6,0,TRUE) = 1
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 +
==Related Videos==
 +
 
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{{#ev:youtube|JR-1ftUj__Y|280|center|POISSON}}
  
 
==See Also==
 
==See Also==
 
*[[Manuals/calci/EXPONDIST  | EXPONDIST ]]
 
*[[Manuals/calci/EXPONDIST  | EXPONDIST ]]
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==References==
 
==References==
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[http://en.wikipedia.org/wiki/Poisson_distribution Poisson distribution ]

Latest revision as of 19:46, 19 June 2015

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)} , 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 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 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 0} 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 x} (included).
  • If it is FALSE, this function will give the Poisson Probability Mass function with the number of events occurring will be exactly 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} .
  • 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 f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}} 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   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
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

References

Poisson distribution

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