Random Variation in a Model

Lognormal

The density function of the lognormal distribution is

\[ f(x) = \frac{1}{x\sqrt {2\pi \sigma ^2}}\mbox{exp}\left(\frac{-(\mbox{ln}(x) - \mu )^2}{2\sigma ^2}\right) \]

where $x > 0$.

Parameters:

$\mu $

is the mean of $\mbox{ln}(x) \sim \mbox{Normal}(\mu , \sigma ^2)$.

$\sigma $

is the standard deviation of $\mbox{ln}(x) \sim \mbox{Normal}(\mu , \sigma ^2)$, $\sigma > 0$.

Table B.14 shows how the lognormal distribution parameter names are specified in Simulation Studio (specifically, in the Numeric Source block) and in JMP.

Table B.14: Lognormal Distribution Parameter Names

 

Simulation Studio

JMP

$\mu $

Mean

$\mu $

$\sigma $

Std Dev

$\sigma $


The following examples show (case-sensitive) string values that can be used as Numeric Source block DataStreamDescription factor values or InStreamPolicy port values. In these examples, the distribution and parameter names in the string value are the names that are used in the Theoretical option in the Numeric Source Block Properties dialog box (including any spaces or hyphens). Quotation marks are not required around the string value, and you can specify only the parameters that need to be updated (as demonstrated in the second example).

  • class == Lognormal;Mean == 0;Std Dev == 0.5

  • Std Dev == 0.25