Difference between revisions of "Manuals/calci/LOGNORMDIST"
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==Examples== | ==Examples== | ||
| − | #LOGNORMDIST(2,5.4,2.76)=0.044061652 | + | #=LOGNORMDIST(2,5.4,2.76) = 0.044061652 |
| − | #LOGNORMDIST(10,24.05,12.95)=0.046543186 | + | #=LOGNORMDIST(10,24.05,12.95) = 0.046543186 |
| − | #LOGNORMDIST(50,87.0036,42.9784)=0.026597569 | + | #=LOGNORMDIST(50,87.0036,42.9784) = 0.026597569 |
| − | #LOGNORMDIST(-10,5,2)=NAN | + | #=LOGNORMDIST(-10,5,2) = NAN |
==See Also== | ==See Also== | ||
Revision as of 05:33, 1 January 2014
LOGNORMDIST(x,m,sd)
- 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 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 m } is the mean 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)} ,
- 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 sd} is the standard deviation 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)} .
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 x \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 sd \le 0}
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