Difference between revisions of "Manuals/calci/LOGNORMDIST"

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<div style="font-size:30px">'''LOGNORMDIST(x,m,sd)'''</div><br/>
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<div style="font-size:30px">'''LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)'''</div><br/>
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*<math>x</math> is the value ,<math> m </math> is the mean of <math>log(x)</math>,
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*<math>Number</math> is the value.
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*And <math> sd</math> is the standard deviation of <math>log(x)</math>.
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*<math>Mean </math> is the mean value of <math>log(x)</math>,
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*<math>StandardDeviation</math> is the standard deviation value of <math>log(x)</math>.
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*<math>Accuracy</math> is correct decimal places for the result.
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** LOGNORMDIST(), returns the cumulative lognormal distribution.
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==Description==
 
==Description==
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*This function gives the value of the cumulative log normal distribution.
 
*This function gives the value of the cumulative log normal distribution.
 
*This  distribution is the continuous probability distribution.  
 
*This  distribution is the continuous probability distribution.  
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*Suppose <math>x</math> is Normally Distributed function, then <math> y=ln(x)</math> also Normally Distributed  
 
*Suppose <math>x</math> is Normally Distributed function, then <math> y=ln(x)</math> also Normally Distributed  
 
*<math> z=exp(y)</math> also Normally Distributed.  
 
*<math> z=exp(y)</math> also Normally Distributed.  
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*Let the Normal Distribution function <math>x</math> and its Mean= <math>μ</math>, Standard Deviation = <math>σ</math>
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*Let the Normal Distribution function <math>x</math> and its Mean= <math>\mu</math>, Standard Deviation = <math>\sigma</math>
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*Then the  lognormal cumulative distribution is calculated by:<math>F(x,μ,σ)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-μ)}{σ\sqrt{2}}\right)\right ]= \phi\left[\frac{ln(x)-μ}{σ}\right ]</math>
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*Then the  lognormal cumulative distribution is calculated by:
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<math>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 ]</math>
 
where <math>erf</math> 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.
 
where <math>erf</math> 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 <math>\phi</math> is the Cumulative Distribution function of the Standard Normal distribution.  
 
*And <math>\phi</math> is the Cumulative Distribution function of the Standard Normal distribution.  
 
*This function will give the result as error when
 
*This function will give the result as error when
 
  1. Any one of the argument is non-numeric.
 
  1. Any one of the argument is non-numeric.
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  2. Suppose <math> x \le 0 </math> or <math> sd \le 0</math>
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  2. Suppose <math> Number \le 0 </math> or <math> StandardDeviation \le 0</math>
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==ZOS==
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*The syntax is to calculate cumulative log normal distribution in ZOS is <math>LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)</math>.
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**<math>Number</math> is the value.
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**<math>Mean </math> is the mean value of <math>log(x)</math>.
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**<math> StandardDeviation</math> is the standard deviation value of <math>log(x)</math>.
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*For e.g.,LOGNORMDIST(10,8.002,4.501)
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{{#ev:youtube|rFnzI4pLSuo|280|center|Log Normal Distribution}}
  
 
==Examples==
 
==Examples==
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#LOGNORMDIST(2,5.4,2.76)=0.044061652
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#=LOGNORMDIST(2,5.4,2.76) = 0.044061652
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#LOGNORMDIST(10,24.05,12.95)=0.046543186
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#=LOGNORMDIST(10,24.05,12.95) = 0.046543186
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#LOGNORMDIST(50,87.0036,42.9784)=0.026597569
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#=LOGNORMDIST(50,87.0036,42.9784) = 0.026597569
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#LOGNORMDIST(-10,5,2)=NAN
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#=LOGNORMDIST(-10,5,2) = #N/A (NUMBER GREATER THAN (OR) NOT EQUAL TO 0)
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==Related Videos==
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{{#ev:youtube|9rMpraPPQ2A|280|center|Lognormal Distribution}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Log-normal_distribution Log-normal distribution]
 
[http://en.wikipedia.org/wiki/Log-normal_distribution Log-normal distribution]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 09:22, 2 June 2020

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)} .
  • 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 Accuracy} is correct decimal places for the result.
    • LOGNORMDIST(), returns the cumulative lognormal distribution.

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 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 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)} .
  • For e.g.,LOGNORMDIST(10,8.002,4.501)
Log Normal Distribution

Examples

  1. =LOGNORMDIST(2,5.4,2.76) = 0.044061652
  2. =LOGNORMDIST(10,24.05,12.95) = 0.046543186
  3. =LOGNORMDIST(50,87.0036,42.9784) = 0.026597569
  4. =LOGNORMDIST(-10,5,2) = #N/A (NUMBER GREATER THAN (OR) NOT EQUAL TO 0)

Related Videos

Lognormal Distribution

See Also

References

Log-normal distribution



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