Manuals/calci/LOGNORMDIST

LOGNORMDIST(x,m,sd)

• $x$ is the value ,$m$ is the mean of $log(x)$,
• And $sd$ is the standard deviation of $log(x)$.

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 $x$ is Normally Distributed function, then $y=ln(x)$ also Normally Distributed
• $z=exp(y)$ also Normally Distributed.
• Let the Normal Distribution function $x$ 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 (syntax error): {\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 $erf$ 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 $\phi$ 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 $x\leq 0$ or $sd\leq 0$

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)=NAN

See Also

• LN
• LOG10
• EXP

References

Log-normal distribution