Difference between revisions of "Manuals/calci/EXPONDIST"

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*This describes the time between events in a Poisson process i.e, a process in which events occur continuously and independently at a constant average rate.
 
*This describes the time between events in a Poisson process i.e, a process in which events occur continuously and independently at a constant average rate.
 
*For e.g Time between successive vehicles arrivals at a workshop.  
 
*For e.g Time between successive vehicles arrivals at a workshop.  
−
*In EXPONDIST(x,\lambda,cu), <math>x</math> is the value of the function, <math>\lambda</math> is called rate parameter and <math>cu</math>(cumulative) is the TRUE or FALSE.
+
*In <math>EXPONDIST(x,\lambda,cu)</math>, <math>x</math> is the value of the function, <math>\lambda</math> is called rate parameter and <math>cu</math>(cumulative) is the TRUE or FALSE.
 
*This function will give the Cumulative Distribution Function when <math>cu</math> is TRUE, otherwise it will give the Probability Density Function , when <math>cu</math> is FALSE.  
 
*This function will give the Cumulative Distribution Function when <math>cu</math> is TRUE, otherwise it will give the Probability Density Function , when <math>cu</math> is FALSE.  
 
*Suppose we are not giving the <math>cu</math> value, by default it will consider the <math>cu</math> value is FALSE.  
 
*Suppose we are not giving the <math>cu</math> value, by default it will consider the <math>cu</math> value is FALSE.  

Revision as of 03:36, 4 December 2013

EXPONDIST(x,lambda,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 value of the function
  • is the value of the rate parameter
  • 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 Exponential Distribution. This distribution is used to model the time until something happens in the process.
  • This describes the time between events in a Poisson process i.e, a process in which events occur continuously and independently at a constant average rate.
  • For e.g Time between successive vehicles arrivals at a workshop.
  • 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 EXPONDIST(x,\lambda,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 value of the function, 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 called rate 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 cu} (cumulative) is the TRUE or FALSE.
  • This function will give the Cumulative Distribution Function 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 cu} is TRUE, otherwise it will give the Probability Density Function , 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 cu} is FALSE.
  • Suppose we are not giving the value, by default it will consider 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 cu} value is FALSE.
  • This function will give the error result 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 \lambda}
 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 \lambda \le 0}

The Probability Density Function of an Exponential Distribution 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)=\lambda e^{-\lambda x} , x \ge 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 =0 , 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 f(x;\lambda)= \lambda e^{-\lambda x} .H(x)}
  • 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 rate 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 H(x)} is the Heaviside step function
  • This function is valid only on the interval [0,infinity].

The Cumulative Distribution 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)=1-e^{-\lambda x}, x \ge 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 0 , 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 F(x,\lambda)=1-e^{-\lambda x}.H(x)}
  • The mean or expected value of the Exponential Distribution 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 E[x]=\frac{1}{\lambda}}
  • The variance of the Exponential Distribution 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 Var[x]=\frac{1}{\lambda^2}} .

Examples

Question : If jobs arrive at an average of 15 seconds, 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 =5} per minute, what is the probability of waiting 30 seconds, i.e 0.5 min? Here 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 =5} 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=0.5}

  • =EXPONDIST(0.5,5,TRUE) = 0.917915001
  • =EXPONDIST(5,3,TRUE) = 0.999999694
  • =EXPONDIST(0.4,2,FALSE) = 0.898657928"

See Also

References

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