Turning Equations into Functions in NetLogo

While some programming languages, such as R, offer many native functions, others (e.g., NetLogo) offer fewer built-in options. However, users can create their own functions easily. Here, we will show the example of a Weibull density distribution function & associated cumulative density distribution function—both not yet implemented in NetLogo or NetLogo extensions.

Density distribution function

Let’s first take a look at the Weibull density distribution function:

\[\begin{equation} f(x) = \frac{\gamma} {\alpha} (\frac{x-\mu} {\alpha})^{(\gamma - 1)}\exp{(-((x-\mu)/\alpha)^{\gamma})} \hspace{.3in} x \ge \mu; \gamma, \alpha > 0 \end{equation}\]

R

In R, this is already implemented:

scale <- 3
shape <- 1

dweibull(scale, shape = shape)

[1] 0.04978707

NetLogo

In Netlogo we can simply translate the mathematical equation into a function:

to-report weibull [a_scale a_shape x]

  let Wei (a_shape / a_scale ) * ((x / a_scale)^(a_shape - 1)) * exp( - ((x / a_scale)^ a_shape))

  report Wei

end

Cumulative density function

Let’s also take a look at the Weibull cumulative density function:

\[\begin{equation} F(x) = 1 - e^{-(x^{\gamma})} \hspace{.3in} x \ge 0; \gamma > 0 \end{equation}\]

R

Again, fully implemented in R already:

scale <- 3
shape <- 1
x <- 5

pweibull(q = x, scale = scale, shape = shape)

[1] 0.8111244

NetLogo

In NetLogo we can simply translate the mathematical equation into a function:

to-report weibull_cumulative [a_scale a_shape x]

  let Wei_cumu 1 - exp( - ((x / a_scale)^ a_shape))

  report Wei_cumu

end