Elicit Distributions
Assists with the construction of probability distributions built from expert elicited data for use in monte carlo simulations.
Usage
Until this is packaged for pip, copy elicit_distibutions.py in your code. Then:
import elicited
elicited is just a helper tool when using numpy and scipy, so you’ll need these too.
import numpy as np
import scipy
Lognormal
See Occurance and Applications for examples of lognormal distributions in nature.
Expert: I have assets at risk that would generate a wide range of losses.
Elicitor: What is the most common value of these assets?
Expert: About $ 20K (
val_mod)Elicitor: What’s the largest asset value you can imagine?
Expert: I suppose it could go as high as $2.5M (
val_max)
Lognormal requires mean and standard deviation.
logN_mean, logN_stdv = elicitLogNormal(val_mod, val_max)
Pareto
The 80/20 rule. See Occurance and Applications
Expert: The legal costs of an incident could be devastating.
Elicitor: How devastating are we talking?
Expert: Well, typically costs are zero (
val_min), but a black swan could be $100M (val_max).Elicitor: So we can assume yoru minimum legal costs for an incident are zero, and your maximum costs are $100M?
Expert: Sure.
b = elicitPareto(val_min, val_max)
p = pareto(b, loc=val_min-1., scale=1.))
PERT
Expert: We have accounts that could be lost and result in losses.
Elicitor: What is the dollar value of these accounts?
Expert: About $500-$6000 (
val_min/val_max).Elicitor: What’s the most common account? (
val_mod)Expert: Probably around $4500.
PERT_a, PERT_b = elicitPERT(val_min, val_mod, val_max)
pert = beta(PERT_a, PERT_b, loc=val_min, scale=val_max-val_min)
Poisson
This is done in numpy without assistance from elicitor. As a courtesy for those looking to use it, here’s an example.
Example Code
Zipf’s
See Applications
Expert: We are concerned about lawsuits relatd to a breach.
Elicitor: Assuming a breach happens, how many litigants will there be?
Expert: One or a few. We could also see an Equifax-like situation. (
nMin)Elicitor: So most likely only a handful of litigants. What’s a nightmare situation?
Expert: I’d guess maybe 30 or more litigants? (
nMax)Elicitor: How likely would it be to have more than 30 litigants?
Expert: Very unlikely, most cases would only have a few, as I said.
Elicitor: Let’s give it a number. Is it one-in-a-thousand, or million cases?
Expert: I’d say one in a million cases. (
pMax)
Zs = elicitZipf(nMin, nMax, pMax, report=True)
pd = zipf(Zs, nMin-1)
