Difference between revisions of "Manuals/calci/POISSONDISTRIBUTION"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''RANDOMNUMBERGENERATION'''(Number, RandomNumber, Distribution,  NewTableFlag, Lambda) where, '''Number '''-...")
 
 
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<div id="6SpaceContent" class="zcontent" align="left">
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<div style="font-size:30px">'''POISSONDISTRIBUTED(a,b)'''</div><br/>
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*<math>a</math> is the number of random numbers to display.
  
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'''RANDOMNUMBERGENERATION'''(Number, RandomNumber, Distribution,  NewTableFlag, Lambda)
+
==Description==
 +
*This function shows the random variables of Poisson distribution.
 +
*It is a discrete frequency distribution which gives the probability of a number of independent events occurring in a fixed time.
 +
*A Poisson random variable is the number of successes that result from a Poisson experiment.
 +
*The probability distribution of a Poisson random variable is called a Poisson distribution.
 +
*Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is <math>\mu</math>.
 +
*Then, the Poisson probability is:
 +
<math>P(x;\mu) = \frac{(e^{-\mu}) (\mu^x)}{ x!}</math>
 +
*where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
 +
*The Poisson distribution has the following properties:
 +
#The mean of the distribution is equal to <math>\mu</math> .
 +
#The variance is also equal to <math>\mu</math> .
 +
*This function will give the result as error when b<0 and a value is not an integer.
  
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where,
+
==Examples==
 +
#POISSONDISTRIBUTED(2,3) =  2  4
 +
#POISSONDISTRIBUTED(7,23) = 23 26 22 22 24 23 20
 +
#POISSONDISTRIBUTED(3,-7) = Null
  
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'''Number '''- represents the number of variables.
+
==See Also==
 +
*[[Manuals/calci/poisson  | poisson ]]
 +
*[[Manuals/calci/EXPONDIST  | EXPONDIST ]]
  
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'''RandomNumber '''- represents the number of random number
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==References==
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+
[http://stattrek.com/probability-distributions/poisson.aspx  Poisson Probability Distribution ]
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'''Distribution '''- represents the distribution method(i.e poisson) to create random values.
 
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'''NewTableFlag''' - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE.
 
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'''Lambda '''- represents the probability value and should be in range 0 to 1.
 
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</div>
 
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----
 
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<div id="1SpaceContent" class="zcontent" align="left">A poisson distribution is a distribution  of random occurrences in which one occurrence has no influence on any other occurrence.</div>
 
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----
 
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<div id="7SpaceContent" class="zcontent" align="left">
 
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Lets see an example in (Column1Row1)
 
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<nowiki>=RANDOMNUMBERGENERATION(3, 4, "Poisson", TRUE, 0.8)</nowiki>
 
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RANDOMNUMBERGENERATION returns the result in new sheet(13Space).
 
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<nowiki>=RANDOMNUMBERGENERATION(5, 4, "Poisson", TRUE, 0.3, -1)</nowiki>
 
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RANDOMNUMBERGENERATION returns the #ERROR(Lambda &lt; 0).
 
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</div>
 
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----
 
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
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RANDOM NUMBER GENERATION : POISSON
 
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</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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----
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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----
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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----
 
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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="8SpaceContent" class="zcontent" align="left">
 
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If Number &lt; 0 or RandomNumber &lt; 0, RANDOMNUMBERGENERATION returns the #ERROR.
 
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RANDOMNUMBERGENERATION returns the #ERROR, if Lambda &lt; 0.
 
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</div>
 
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<div id="5SpaceContent" class="zcontent" align="left">
 
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{| id="TABLE1" class="SpreadSheet blue"
 
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|+ Random Number Generation<br />Binomial Distribution
 
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|- class="even"
 
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| 0
 
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|- class="odd"
 
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</div>
 
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<div id="9SpaceContent" class="zcontent" align="left">
 
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{| id="TABLE2" class="SpreadSheet blue"
 
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|+ Random Number Generation<br />Poisson Distribution
 
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</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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|+ Default Calci
 
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|- class="even"
 
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| class=" " |
 
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| Column1
 
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| Column2
 
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| Column3
 
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| Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class="sshl_f" | 13Space
 
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| class=" " |
 
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| class=" " |
 
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| class=" " |
 
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|- class="even"
 
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| class="  " | Row2
 
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| class="sshl_f" | #ERROR
 
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|- class="odd"
 
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| class=" " | Row5
 
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| class="  SelectTD1 ChangeBGColor SelectTD1" |
 
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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>
 
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| class=" " |
 
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{|
 
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| <span align="left">[[Image:calci1.gif]]</span>
 
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[[Image:bold.gif]]
 
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[[Image:italic.gif]]
 
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[[Image:normal.gif]]
 
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[[Image:underline.gif]]
 
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[[Image:border.gif]]
 
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[[Image:numbers.gif]]
 
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[[Image:sort.gif]]
 
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[[Image:formatcells.gif]]
 
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[[Image:graphs.gif]]
 
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| $
 
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|}
 
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</div>
 
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----
 
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<div id="13SpaceContent" class="zcontent" align="left">
 
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{| class="SpreadSheet blue"
 
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|+ Random Number Generation<br />Poisson Distribution
 
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|- class="even"
 
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| 0
 
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| 0
 
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| 0
 
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|- class="odd"
 
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| 1
 
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| 0
 
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| 1
 
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|- class="even"
 
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| 0
 
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|}
 
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</div>
 
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----
 

Latest revision as of 06:56, 27 October 2015

POISSONDISTRIBUTED(a,b)


  • is the number of random numbers to display.

Description

  • This function shows the random variables of Poisson distribution.
  • It is a discrete frequency distribution which gives the probability of a number of independent events occurring in a fixed time.
  • A Poisson random variable is the number of successes that result from a Poisson experiment.
  • The probability distribution of a Poisson random variable is called a Poisson distribution.
  • Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is .
  • Then, the Poisson probability is:

  • where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
  • The Poisson distribution has the following properties:
  1. The mean of the distribution is equal to .
  2. The variance is also equal to .
  • This function will give the result as error when b<0 and a value is not an integer.

Examples

  1. POISSONDISTRIBUTED(2,3) = 2 4
  2. POISSONDISTRIBUTED(7,23) = 23 26 22 22 24 23 20
  3. POISSONDISTRIBUTED(3,-7) = Null

See Also

References

Poisson Probability Distribution

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