Manuals/calci/LOGNORMDIST

LOGNORMDIST(number,mean,standarddeviation)

• $number$ is the value.
• $mean$ is the mean value of $log(x)$,
• $standarddeviation$ is the standard deviation value 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= $\mu$, Standard Deviation = $\sigma$
• Then the lognormal cumulative distribution is calculated by:

$F(x,\mu ,\sigma )={\frac {1}{2}}\left[1+erf\left({\frac {ln(x)-\mu )}{\sigma {\sqrt {2}}}}\right)\right]=\varphi \left[{\frac {ln(x)-\mu }{\sigma }}\right]$ where $erf$ 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 $number\leq 0$ or $standarddeviation\leq 0$

ZOS Section

• The syntax is to calculate cumulative log normal distribution in ZOS is $LOGNORMDIST(number,mean,standarddeviation)$.
  • $number$ is the value.
  • $mean$ is the mean value of $log(x)$.
  • $standarddeviation$ is the standard deviation value of $log(x)$.
• 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) = NAN

See Also

• LN
• LOG10
• EXP

References

Log-normal distribution