Random Variation in a Model

Erlang

The Erlang distribution is a special case of the gamma distribution . The density function of the Erlang distribution is

\[ f(x) = \frac{1}{(k - 1)!}\lambda ^{-k}x^{k - 1}e^{-\frac{x}{\lambda }} \]

where $x \ge 0$.

Parameters:

$\lambda $

is a real number > 0.

k

is an integer $\ge $ 1.

If $X_1, X_2, \dots , X_ k$ are independent exponential random variables with mean $\lambda $, then $X_1 + X_2 + \dots + X_ k$ has the k-Erlang distribution.

Table B.8 shows how the erlang distribution parameter names are specified in Simulation Studio (specifically, in the Numeric Source block). The erlang distribution is not available with the Distribution option in JMP.

Table B.8: Erlang Distribution Parameter Names

 

Simulation Studio

JMP

k

K

–

$\lambda $

Lambda

–


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 == Erlang;K == 2;Lambda == 1.0

  • K == 3