Manuals/calci/POISSONDISTRIBUTION

POISSONDISTRIBUTED(a,b)

• $a$ 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 $\mu$.
• Then, the Poisson probability is:

$P(x;\mu )={\frac {(e^{-\mu })(\mu ^{x})}{x!}}$

• 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 $\mu$ .
2. The variance is also equal to $\mu$ .

• 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

RANDOMNUMBERGENERATION(Number, RandomNumber, Distribution,  NewTableFlag, Lambda)

where,

Number - represents the number of variables.

RandomNumber - represents the number of random number

Distribution - represents the distribution method(i.e poisson) to create random values.

NewTableFlag - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE.

Lambda - represents the probability value and should be in range 0 to 1.

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A poisson distribution is a distribution  of random occurrences in which one occurrence has no influence on any other occurrence.

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Lets see an example in (Column1Row1)

?UNIQa09fd274c5c89988-nowiki-00000004-QINU?

RANDOMNUMBERGENERATION returns the result in new sheet(13Space).

?UNIQa09fd274c5c89988-nowiki-00000005-QINU?

RANDOMNUMBERGENERATION returns the #ERROR(Lambda < 0).

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RANDOM NUMBER GENERATION : POISSON

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Syntax

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Remarks

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Examples

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Description

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If Number < 0 or RandomNumber < 0, RANDOMNUMBERGENERATION returns the #ERROR.

RANDOMNUMBERGENERATION returns the #ERROR, if Lambda < 0.

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Random Number Generation
Binomial Distribution

0	1	1
1	0	2
0	2	1
1	1	1

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Random Number Generation
Poisson Distribution

0	0	1
1	1	2
0	1	0
2	2	1

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Default Calci

	Column1	Column2	Column3	Column4
Row1	13Space
Row2
Row3
Row4	#ERROR
Row5	File:Copy-cube.gif
Row6

File:Calci1.gif

$

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Random Number Generation
Poisson Distribution

0	0	0
1	0	1
1	0	1
0	0	0

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