Difference between revisions of "Manuals/calci/LOGNORMDIST"
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*<math> z=exp(y)</math> also Normally Distributed. | *<math> z=exp(y)</math> also Normally Distributed. | ||
*Let the Normal Distribution function <math>x</math> and its Mean= <math>μ</math>, Standard Deviation = <math>σ</math> | *Let the Normal Distribution function <math>x</math> and its Mean= <math>μ</math>, Standard Deviation = <math>σ</math> | ||
| − | *Then the lognormal cumulative distribution is calculated by:<math>F(x, | + | *Then the lognormal cumulative distribution is calculated by:<math>F(x,\mu,\sigma)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-μ)}{σ\sqrt{2}}\right)\right ]= \phi\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. | ||
Revision as of 00:15, 31 December 2013
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 μ} , 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 σ}
- 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)-μ)}{σ\sqrt{2}}\right)\right ]= \phi\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.
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