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

The syntax is to calculate cumulative log normal distribution in ZOS is .
- $number$ 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)