Difference between revisions of "Manuals/calci/NORMAL"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''RANDOMNUMBERGENERATION'''(Number, RandomNumber, Distribution, NewTableFlag, Mean, StandardDeviation) where, ...")
 
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<div style="font-size:30px">'''NORMALDISTRIBUTED(x,m,sd)'''</div><br/>
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*<math>x</math>  is the value for which distribution is evaluated.
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*<math>m </math> is the mean.
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*<math>sd</math> is the standard deviation.
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 +
 +
==Description==
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*This function gives the value of the normal  probability distribution.
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*It is the  continuous probability distribution.
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*The normal distributions are a very important class of statistical distributions.
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*All normal distributions are symmetric and have bell-shaped density curves with a single peak.
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*The term bell curve is used to describe the mathematical concept called normal distribution.
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*It is also called as Gaussian distribution.
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*The Normal Distribution has: mean = median = mode
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*i.e., This distribution is symmetry about the center.
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*Half of values less than the mean and half of values greater than the mean.
 +
*In a normal distribution the probability values are satisfying the following conditions:
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  1. The total area under the curve is equal to 1 (100%)
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  2. About 68% of the area under the curve falls within 1 standard deviation.
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  3. About 95% of the area under the curve falls within 2 standard deviations.
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  4. About 99.7% of the area under the curve falls within 3 standard deviations.
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*In a normal distribution the mean =0 and standard deviation =1,then  the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.
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*It is the only absolutely continuous distribution.
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*A normal distribution is calculated by
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<math>f(x,\mu,\sigma)=\frac {1}{\sigma\sqrt(2\pi) e^{\frac{-(x-\mu)^2}{2\sigma^2}, where <math>\mu</math> is the mean and  <math>\sigma<\math> is the standard deviaton of the distribution.
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 +
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where  ,  and 
 
<div id="6SpaceContent" class="zcontent" align="left">
 
<div id="6SpaceContent" class="zcontent" align="left">
  
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Lets see an example in (Column3Row1)
 
Lets see an example in (Column3Row1)
  
<nowiki>=RANDOMNUMBERGENERATION(3, 4, "Normal", TRUE, 0, 4)</nowiki>
+
UNIQeebbe8a3183fa626-nowiki-00000004-QINU
  
 
RANDOMNUMBERGENERATION returns the result in new sheet(5Space).
 
RANDOMNUMBERGENERATION returns the result in new sheet(5Space).
  
<nowiki>=RANDOMNUMBERGENERATION(-3, 4, "Uniform", TRUE, 3, 4)</nowiki>
+
UNIQeebbe8a3183fa626-nowiki-00000005-QINU
  
 
RANDOMNUMBERGENERATION returns the #ERROR(Number &lt; 0).
 
RANDOMNUMBERGENERATION returns the #ERROR(Number &lt; 0).

Revision as of 01:50, 24 March 2014

NORMALDISTRIBUTED(x,m,sd)


  • is the value for which distribution is evaluated.
  • is the mean.
  • is the standard deviation.


Description

  • This function gives the value of the normal probability distribution.
  • It is the continuous probability distribution.
  • The normal distributions are a very important class of statistical distributions.
  • All normal distributions are symmetric and have bell-shaped density curves with a single peak.
  • The term bell curve is used to describe the mathematical concept called normal distribution.
  • It is also called as Gaussian distribution.
  • The Normal Distribution has: mean = median = mode
  • i.e., This distribution is symmetry about the center.
  • Half of values less than the mean and half of values greater than the mean.
  • In a normal distribution the probability values are satisfying the following conditions:
 1. The total area under the curve is equal to 1 (100%) 
 2. About 68% of the area under the curve falls within 1 standard deviation.
 3. About 95% of the area under the curve falls within 2 standard deviations.
 4. About 99.7% of the area under the curve falls within 3 standard deviations. 
  • In a normal distribution the mean =0 and standard deviation =1,then the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.
  • It is the only absolutely continuous distribution.
  • A normal distribution is calculated by

Failed to parse (syntax error): {\displaystyle f(x,\mu,\sigma)=\frac {1}{\sigma\sqrt(2\pi) e^{\frac{-(x-\mu)^2}{2\sigma^2}, where <math>\mu} is the mean and <math>\sigma<\math> is the standard deviaton of the distribution.


where , and

RANDOMNUMBERGENERATION(Number, RandomNumber, Distribution, NewTableFlag, Mean, StandardDeviation)

where,

Number - represents the number of variables.

RandomNumber - represents the number of random number.

Distribution - represents the distribution method(i.e normal) 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.

Mean - represents the Mean.

StandardDeviation - represents the standard deviation.


Normal Distribution characterized by a mean and a standard deviation.

Lets see an example in (Column3Row1)

?UNIQeebbe8a3183fa626-nowiki-00000004-QINU?

RANDOMNUMBERGENERATION returns the result in new sheet(5Space).

?UNIQeebbe8a3183fa626-nowiki-00000005-QINU?

RANDOMNUMBERGENERATION returns the #ERROR(Number < 0).


RANDOM NUMBER GENERATION : NORMAL


Syntax

Remarks

Examples

Description

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


Column1 Column2 Column3 Column4
Row1 5Space
Row2
Row3
Row4
Row5
Row6

Random Number Generation
Normal Distribution
-0.6469271541994427 -1.9074080903736057 -0.617997136104105
-0.7646726307858795 -0.12686814329075044 -1.0016839542241755
1.5847698409152808 0.6334613031585946 -0.4798269568260549
-1.6687086155351085 1.102906962994111 1.4347768240383833