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Difference between revisions of "Manuals/calci/EXPONDIST"

(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> <font size="3"><font face="Times New Roman">'''EXPONDIST'''('''x''',''' Lambda, cum''')</font></font> <font size="...")
 
 
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<div id="6SpaceContent" class="zcontent" align="left">
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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>Lambda(\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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**EXPONDIST(), returns the exponential distribution.
  
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<font size="3"><font face="Times New Roman">'''EXPONDIST'''('''x''',''' Lambda, cum''')</font></font>
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==Description==
 +
*This function gives the  Exponential Distribution. This distribution is used to model the time until something happens in the process.
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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.
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*For e.g Time between successive vehicles arrivals at a workshop.
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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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*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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*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.
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*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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2. <math>X<0</math> or <math>Lambda \le 0</math>
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The Probability Density Function of an Exponential Distribution is:
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<math>f(x,\lambda)=\begin{cases}
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\lambda e^{-\lambda x} &, x \ge 0 \\
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0 &, x<0
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\end{cases}</math>
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or 
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:<math>f(x;\lambda)= \lambda e^{-\lambda x} .H(x)</math>
  
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<font size="3"><font face="Times New Roman">Where X is the value of the function, Lambda is the parameter value and Cumulative is a logical value.</font></font>
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*where <math>\lambda</math> is the rate parameter and <math>H(x)</math> is the Heaviside step function
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*This function is valid only on the interval [0,infinity].
 +
The Cumulative Distribution Function is :
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<math>F(x,\lambda)=\begin{cases}
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1-e^{-\lambda x} &, x \ge 0 \\
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0 &, x<0
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\end{cases}</math>
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or
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:<math>F(x,\lambda)=1-e^{-\lambda x}.H(x)</math>
  
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</div>
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==ZOS==
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----
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*The syntax is to calculate EXPONDIST in ZOS is <math>(X,Lambda,Cumulative)</math>.
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<div id="1SpaceContent" class="zcontent" align="left">
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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}}
  
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<font size="3"><font face="Times New Roman">EXPONDIST is to model the time between events.</font></font>
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==Examples==
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Question : If jobs arrive at an average of 15 seconds, <math>\lambda =5</math> per minute, what is the probability of waiting 30 seconds, i.e 0.5 min?
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Here <math>\lambda =5</math> and <math>x=0.5</math>
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*=EXPONDIST(0.5,5,TRUE) = 0.917915001
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*=EXPONDIST(5,3,TRUE) = 0.999999694
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*=EXPONDIST(0.4,2,FALSE) = 0.898657928
  
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</div>
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==Related Videos==
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<div id="7SpaceContent" class="zcontent" align="left">
 
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">X or Lambda must be a numeric value in this function. Otherwise it shows error.</font></font>
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{{#ev:youtube|RQ9VOaWxDFo|280|center|Exponential Probability}}
  
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<font size="3">·</font>        <font size="3"><font face="Times New Roman">If x is less than 0, or Lambda less than or equal to zero, EXPONDIST shows error value. </font></font>
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==See Also==
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*[[Manuals/calci/GAMMADIST| GAMMADIST]]
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*[[Manuals/calci/POISSONDISTRIBUTION| POISSONDISTRIBUTION]]
  
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</div>
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==References==
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----
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*[http://en.wikipedia.org/wiki/Exponential_distribution  Exponential Distribution]
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">EXPONDIST</div></div>
 
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----
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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<div id="2SpaceContent" class="zcontent" align="left">
 
  
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{| id="TABLE3" class="SpreadSheet blue"
 
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|- class="even"
 
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<div id="2Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
 
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| class="  " | Column1
 
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| class="        SelectTD ChangeBGColor SelectTD" |
 
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<div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]]</div>Column2
 
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| class="  " | Column3
 
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| class="  " | Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class=" " | 0.5
 
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|- class="even"
 
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| class="sshl_f" | Row@
 
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| class=" " | 15
 
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| class="sshl_f  " |
 
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| class="sshl_f" |
 
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|- class="odd"
 
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| class="sshl_f" | 0.999447
 
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| class="sshl_f" |
 
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|- class="even"
 
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| class="sshl_f" | Row3
 
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| class="sshl_f" | 0.008296
 
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<div align="left">[[Image:calci1.gif]]</div></div>
 
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<div id="8SpaceContent" class="zcontent" align="left"><font size="3"><font face="Times New Roman">''' <font size="3"><font face="Times New Roman">AVEDEV (N1, N2...)</font></font> <font size="3"><font face="Times New Roman">Where N1, N 2 ...   are positive integers.</font></font> '''</font></font></div>
 
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<div id="5SpaceContent" class="zcontent" align="left"><font size="3">
 
  
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Let’s see an example
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*[[Z_API_Functions | List of Main Z Functions]]
  
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EXPONDIST(x, Lambda, cum)
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*[[ Z3 |  Z3 home ]]
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B
 
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0.5
 
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15
 
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<nowiki>=EXPONDIST (B2, B3, TRUE) is 0.9994</nowiki>
 
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<nowiki>=EXPONDIST (0.5, 15, FALSE) is 0.0083</nowiki>
 
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</font></div>
 
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Latest revision as of 17:04, 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.   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
    • 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.
  • 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   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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