Since I am not well-versed in mathematics, I am struggling with the implementation of a random number generator in NetLogo which follows roughly a pareto distribution. This is the follow-up question of this one here, where I would like to substitue the random-float with something like "random-pareto" in order to have events taking place in the model following a pareto distribution (thinking of simulated earthquakes and their degree of destructiveness).
The code in question is:
ask hits [
let %draw (random-float 100)
let %strength 0 ;; no damage
if (%draw < 50) [set %strength (%strength + 1)] ;;1 for little damage
if (%draw < 10) [set %strength (%strength + 1)] ;;2 for middle damage
if (%draw < 5) [set %strength (%strength + 1)] ;;3 for strong damage
if (%draw < 1) [set %strength (%strength + 1)] ;;4 for complete destruction
ifelse pcolor = red [die]
[ ask n-of %strength patches [ set pcolor red ]]
]
I got inspired by this question here to do the same in R and the Netlogo Dictionary here about the fact that random-exponential can be written as (- mean) * ln random-float 1.0.
Can somebody help?
What you need is the equation to convert from a uniform distribution (random-float) to the distribution you want. This might be a better question for the stackexchange stats. However, according to Wikipedia, the formula is:
$$ T = \frac{m}{U^\frac{1}{\alpha}} $$
where $U$ is the uniform input, $T$ is the Pareto distributed random number, $m$ (minimum) and $\alpha$ are parameters of the distribution. If this is correct, you could code in NetLogo as
to-report random-pareto [alpha mm]
report mm / ( random-float 1 ^ (1 / alpha) )
end
Say you wanted a random Pareto from the distribution with minimum of 1 and alpha of 3, you could then get one with the code random-pareto 3 1