Difference between revisions of "Manuals/calci/POISSONDISTRIBUTION"

Revision as of 06:47, 27 October 2015

POISSONDISTRIBUTED(a,b)

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:

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.

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

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).

RANDOM NUMBER GENERATION : POISSON

Syntax

Remarks

Examples

Description

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

RANDOMNUMBERGENERATION returns the #ERROR, if Lambda < 0.

$

@@ Line 9: / Line 9: @@
 *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>
+<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: