Helper tools to construct probability distributions built from expert elicited data for use in monte carlo simulations.

Credit to Brett Hoover, packaging by @magoo. This is early code, happy to look at issues and feedback.

Usage

pip install elicited

import elicited as e

elicited is just a helper tool when using numpy and scipy, so you'll need them in your code to pass parameters to distributions you're looking for.

import numpy as np
from scipy.stats import poisson, zipf, beta, pareto, lognorm

Build distributions for monte carlo trials.

# Elicted values from an expert
mode = 20000
max = 2500000
# Parameters for lognormal distribution
mean, stdv = e.elicitLogNormal(mode, max)
# Freeze distribution w/ parameters
asset_values = lognorm(s=stdv, scale=np.exp(mean))
# Draw values from lognormal distribution
asset_values.rvs(100)

Lognormal

elicitLogNormal takes a mode, and a value at quantile max. The default max quantile is a 95% percentile estimate, and can be changed with quantP.

See Occurance and Applications for examples of lognormal distributions in nature, and elicited technical docs.

Expert: Most customers hold around $20K (mode) but I could imagine a customer with $2.5M (max)

mode = 20000
max = 2500000
mean, stdv = e.elicitLogNormal(mode, max, quantP=0.95)
asset_values = lognorm(s=stdv, scale=np.exp(mean))
asset_values.rvs(100)

PERT

See PERT Distribution, and elicited technical docs.

Expert: Our customers have anywhere from $500-$6000 (val_min / val_max), but it's most typically around $4500 (val_mod)

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)

Pareto

elicitPareto takes a min, and a value at quantile max. The default max quantile is a 95% percentile estimate, and can be changed with quantP.

The 80/20 rule. See Occurance and Applications, and elicited technical docs.

Expert: The legal costs of an incident could be devastating. Typically costs are almost zero (min) but a black swan could be $100M (max).

b = e.elicitPareto(min, max, quantP=0.95)
p = pareto(b, loc=val_min-1., scale=1.))

Zipf's

elicitZipfs takes a min, and a value at quantile max. The default max quantile is a 95% percentile estimate, and can be changed with quantP. This function also has a report argument to report error.

See Applications, and elicited technical docs.

Expert: If we get sued, there will only be a few litigants (min). Very rarely it could be 30 or more litigants (max), maybe once every thousand cases (p) it would be more.

min = 1
max = 30
p = 1/1000
Zs = e.elicitZipf(min, max, quantP=p)
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.

Uniform

A "zero knowledge" distribution where all values within the range have equal probability of appearing. Similar to random.randint(a, b)

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)

Poisson

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)