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Difference between revisions of "Manuals/calci/EXPONDIST"
 
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<div style="font-size:30px">'''EXPONDIST(x,lambda,cu)'''</div><br/>
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<div style="font-size:25px">'''EXPONDIST(X,Lambda,Cumulative)'''</div><br/>
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*<math>x</math> is the value of the function
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*<math>X</math> is the value of the function.
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*<math>lambda(\lambda)</math> is the value of the rate parameter
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*<math>Lambda(\lambda)</math> is the value of the rate parameter.
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*<math>cu</math> is the logical value like TRUE or FALSE
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*<math>Cumulative</math> is the logical value like TRUE or FALSE.
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**EXPONDIST(), returns the exponential distribution.
  
 
==Description==
 
==Description==
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*This function gives the  Exponential Distribution. This distribution is used to model the time until something happens in the process.
 
*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.
 
*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.  
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*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.
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*Exponential distribution is the only continuous memoryless random distribution. It is a continuous analog of the Geometric distribution.
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*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.  
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*In <math>EXPONDIST(X,Lambda,Cumulative)</math>, <math>X</math> is the value of the function, <math> Lambda</math> is called rate parameter and <math>Cumulative</math> is either TRUE or FALSE.
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*Suppose we are not giving the <math>cu</math> value, by default it will consider the <math>cu</math> value is FALSE.  
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*This function will give the Cumulative Distribution Function when <math>Cumulative</math> is TRUE, otherwise it will give the Probability Density Function , when <math>Cumulative</math> is FALSE.  
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*Suppose we are not giving the <math>Cumulative</math> value, by default it will consider the <math>Cumulative</math> value is FALSE.  
 
*This function will give the error result when
 
*This function will give the error result when
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  1. <math>x</math> or <math>lambda</math> is non-numeric.
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  1. <math>X</math> or <math>Lambda</math> is non-numeric.
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  2. <math>x<0</math> or <math>lambda \le 0</math>
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  2. <math>X<0</math> or <math>Lambda \le 0</math>
 
The Probability Density Function of an Exponential Distribution is:
 
The Probability Density Function of an Exponential Distribution is:
 
<math>f(x,\lambda)=\begin{cases}
 
<math>f(x,\lambda)=\begin{cases}
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or
 
or
 
:<math>F(x,\lambda)=1-e^{-\lambda x}.H(x)</math>
 
:<math>F(x,\lambda)=1-e^{-\lambda x}.H(x)</math>
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==ZOS==
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*The syntax is to calculate EXPONDIST in ZOS is <math>(X,Lambda,Cumulative)</math>.
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**where <math>X</math> is the value of the function
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**<math>Lambda</math> is the value of the rate parameter
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**<math>Cumulative</math> is the logical value like TRUE or FALSE.
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*For e.g.,EXPONDIST(11..12,2.3..3.3..0.4,FALSE)
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{{#ev:youtube|R1BjrD7T6Fs|280|center|Exponential Distribution}}
  
 
==Examples==
 
==Examples==
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*=EXPONDIST(0.5,5,TRUE) = 0.917915001
 
*=EXPONDIST(0.5,5,TRUE) = 0.917915001
 
*=EXPONDIST(5,3,TRUE) = 0.999999694
 
*=EXPONDIST(5,3,TRUE) = 0.999999694
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*=EXPONDIST(0.4,2,FALSE) = 0.898657928"
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*=EXPONDIST(0.4,2,FALSE) = 0.898657928
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==Related Videos==
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{{#ev:youtube|RQ9VOaWxDFo|280|center|Exponential Probability}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
 
*[http://en.wikipedia.org/wiki/Exponential_distribution  Exponential Distribution]
 
*[http://en.wikipedia.org/wiki/Exponential_distribution  Exponential Distribution]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 16:04, 10 August 2018

EXPONDIST(X,Lambda,Cumulative)


  • 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(\lambda)} 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 Cumulative} is the logical value like TRUE or FALSE.
    • EXPONDIST(), returns the exponential distribution.

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.
  • Exponential distribution is the only continuous memoryless random distribution. It is a continuous analog of the Geometric distribution.
  • 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,Cumulative)} , 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 Cumulative} is either 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 Cumulative} 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 Cumulative} is FALSE.
  • Suppose we are not giving 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 Cumulative} 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 Cumulative} 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)=\begin{cases} \lambda e^{-\lambda x} &, x \ge 0 \\ 0 &, x<0 \end{cases}} 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)=\begin{cases} 1-e^{-\lambda x} &, x \ge 0 \\ 0 &, x<0 \end{cases}} 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)}

ZOS

  • The syntax is to calculate EXPONDIST in ZOS 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,Lambda,Cumulative)} .
    • 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 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 the value of the rate parameter
    •   is the logical value like TRUE or FALSE.
  • For e.g.,EXPONDIST(11..12,2.3..3.3..0.4,FALSE)
Exponential Distribution

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

Related Videos

Exponential Probability

See Also

References


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