Difference between revisions of "Manuals/calci/LOGNORMDIST"

Revision as of 16:30, 14 June 2018

LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)

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 Number} is the value.
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 Mean } is the mean value of 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 log(x)} ,
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 StandardDeviation} is the standard deviation value of 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 log(x)} .
$Accuracy$ is correct decimal places for the result.

Description

This function gives the value of the cumulative log normal distribution.
This distribution is the continuous probability distribution.
Lognomal distribution is also called Galton's distribution.
A random variable which is log-normally distributed takes only positive real values.
Suppose 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 Normally Distributed function, then 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 y=ln(x)} also Normally Distributed
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 z=exp(y)} also Normally Distributed.
Let the Normal Distribution 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 x} and its Mean= 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 \mu} , Standard Deviation = 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 \sigma}
Then the lognormal cumulative distribution is calculated by:

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,\mu,\sigma)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-\mu)}{\sigma \sqrt{2}}\right)\right ]= \varphi\left[\frac{ln(x)-\mu}{\sigma}\right ]} 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 erf} is the error function,. The error function (also called the Gauss error function) is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations.

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 \phi} is the Cumulative Distribution function of the Standard Normal distribution.
This function will give the result as error when

1. Any one of the argument is non-numeric.
2. Suppose 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  Number \le 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  StandardDeviation \le 0}

ZOS

The syntax is to calculate cumulative log normal distribution 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 Number} is the value.
- 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 Mean } is the mean value of 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 log(x)} .
- 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 StandardDeviation} is the standard deviation value of 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 log(x)} .
For e.g.,LOGNORMDIST(10,8.002,4.501)

Log Normal Distribution

Examples

=LOGNORMDIST(2,5.4,2.76) = 0.044061652
=LOGNORMDIST(10,24.05,12.95) = 0.046543186
=LOGNORMDIST(50,87.0036,42.9784) = 0.026597569
=LOGNORMDIST(-10,5,2) = NAN

References

Log-normal distribution

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''LOGNORMDIST(number,mean,standarddeviation)'''</div><br/>
+<div style="font-size:30px">'''LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)'''</div><br/>
-*<math>number</math> is the value.
+*<math>Number</math> is the value.
-*<math> mean </math> is the mean value of <math>log(x)</math>,
+*<math>Mean </math> is the mean value of <math>log(x)</math>,
-*<math> standarddeviation</math> is the standard deviation value of <math>log(x)</math>.
+*<math>StandardDeviation</math> is the standard deviation value of <math>log(x)</math>.
+*<math>Accuracy</math> is correct decimal places for the result.
 ==Description==
@@ Line 18: / Line 19: @@
 *This function will give the result as error when
 . Any one of the argument is non-numeric.
-. Suppose <math> number \le 0 </math> or <math> standarddeviation \le 0</math>
+. Suppose <math> Number \le 0 </math> or <math> StandardDeviation \le 0</math>
 ==ZOS==
-*The syntax is to calculate cumulative log normal distribution in ZOS is <math>LOGNORMDIST(number,mean,standarddeviation)</math>.
+*The syntax is to calculate cumulative log normal distribution in ZOS is <math>LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)</math>.
-**<math>number</math> is the value.
+**<math>Number</math> is the value.
-**<math> mean </math> is the mean value of <math>log(x)</math>.
+**<math>Mean </math> is the mean value of <math>log(x)</math>.
-**<math> standarddeviation</math> is the standard deviation value of <math>log(x)</math>.
+**<math> StandardDeviation</math> is the standard deviation value of <math>log(x)</math>.
 *For e.g.,LOGNORMDIST(10,8.002,4.501)
 {{#ev:youtube|rFnzI4pLSuo|280|center|Log Normal Distribution}}

Difference between revisions of "Manuals/calci/LOGNORMDIST"

Revision as of 16:30, 14 June 2018

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Description

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Examples

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