Manuals/calci/LOGNORMDIST

LOGNORMDIST(Number,Mean,StandardDeviation,Accuracy)

$Number$ is the value.
$Mean$ is the mean value of $log(x)$ ,
$StandardDeviation$ is the standard deviation value of $log(x)$ .
is correct decimal places for the result.
- LOGNORMDIST(), returns the cumulative lognormal distribution.

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)