Helper tools to construct probability distributions built from expert elicited data for use in monte carlo simulations.
Credit to Brett Hoover, packaging by @magoo
pip install elicited
import elicited as e
elicited is just a helper tool when using numpy and scipy, so you'll need these in your code.
import numpy as np from scipy.stats import poisson, zipf, beta, pareto, lognorm
See Occurance and Applications for examples of lognormal distributions in nature.
Expert: Most customers hold around $20K (
mode) but I could imagine a customer with $2.5M (
mode = 20000 max = 2500000 mean, stdv = e.elicitLogNormal(mode, max) asset_values = lognorm(s=stdv, scale=np.exp(mean)) asset_values.rvs(100)
The 80/20 rule. See Occurance and Applications
Expert: The legal costs of an incident could be devastating. Typically costs are almost zero (
val_min) but a black swan could be $100M (
b = e.elicitPareto(val_min, val_max) p = pareto(b, loc=val_min-1., scale=1.))
Expert: Our customers have anywhere from $500-$6000 (
val_max), but it's most typically around $4500 (
PERT_a, PERT_b = e.elicitPERT(val_min, val_mod, val_max) pert = beta(PERT_a, PERT_b, loc=val_min, scale=val_max-val_min)
Expert: If we get sued, there will only be a few litigants (
nMin). Very rarely it could be 30 or more litigants (
nMax), maybe once every thousand cases (
pMax) it would be more.
nMin = 1 nMax = 30 pMax = 1/1000 Zs = e.elicitZipf(nMin, nMax, pMax, report=True) litigants = zipf(Zs, nMin-1) litigants.rvs(100)
Reference: Other Useful Elicitations
Listed as a courtesy, these distributions are simple enough to elicit data into directly without a helper function.
A "zero knowledge" distribution where all values within the range have equal probability of appearing. Similar to
Expert: The crowd will be between 50 (
min) and 500 (
max) due to fire code restrictions and the existing residents in the building.
from scipy.stats import uniform min = 50 max = 500 range = max - min crowd_size = uniform(min, range) crowd_size.rvs(100)
Expert: About 3000 Customers (
average) add a credit card to their account every quarter.
from scipy.stats import poisson average = 3000 upsells = poisson(average) upsells.rvs(100)