LogNormal Distribution¶

Log-normal¶

The log-normal distribution has the probability density function (PDF):

\[f(x\mid \mu ,\sigma ^{2}) = \frac 1 {x\sigma\sqrt{2\pi}}\ \exp\left(-\frac{\left(\ln x-\mu\right)^2}{2\sigma^2}\right) \,,\quad x>0 \,,\]

where \(\mu\in\mathbb{R}\) and \(\sigma > 0\) are the parameters associated with the Normal distribution. The mean of the PDF is \(\exp(\mu+\frac{\sigma^2}{2})\).

Usage¶

e["Distribution"][*index*]["Type"] = "Univariate/LogNormal"

Distribution Configuration¶

These are settings required by this distribution.

Mu

Usage: e[“Mu”] = real number
Description: Check: https://en.wikipedia.org/wiki/Log-normal_distribution

Sigma

Usage: e[“Sigma”] = real number
Description: Check: https://en.wikipedia.org/wiki/Log-normal_distribution

Configuration¶

These are settings required by this module.

Name

Usage: e[“Name”] = string
Description: Defines the name of the distribution.

Random Seed

Usage: e[“Random Seed”] = unsigned integer
Description: Defines the random seed of the distribution.

Range

Usage: e[“Range”] = gsl_rng
Description: Stores the current state of the distribution in hexadecimal notation.

Default Configuration¶

These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.

{
"Name": "",
"Random Seed": 0,
"Range": ""
}