Working with Distributions

Elicit, fit, plot, and sample

Overview

Every concrete drisk distribution exposes the same small API:

elicit(...) constructs a distribution from expert-provided inputs,
fit(data, ...) estimates distribution parameters from observations,
plot(...) gives a quick visual check of the shape, and
sample(...) generates Monte Carlo draws.

import numpy as np

import drisk as dr

Elicit from expert judgement

Elicitation is useful when you have estimates rather than raw data. For example, an expert might say that a typical delivery time is expected to fall between 8 and 14 days with 80% confidence.

delivery_days = dr.LogNormal.elicit(
    lower=8,
    upper=14,
    confidence=0.8,
    name="Delivery time, days",
)

delivery_days

LogNormal(dist_type='lognormal', name='Delivery time, days', elicitation_params={'lower': 8, 'upper': 14, 'confidence': 0.8}, params={'mu': 2.359249435647547, 'sigma': 0.2183352597667858})

The original elicitation inputs are stored alongside the fitted distribution parameters.

delivery_days.params, delivery_days.elicitation_params

({'mu': 2.359249435647547, 'sigma': 0.2183352597667858},
 {'lower': 8, 'upper': 14, 'confidence': 0.8})

Sample from a distribution

Use .sample() to draw values for a simulation. Pass a seed when you want reproducible examples or tests.

samples = delivery_days.sample(size=10_000, seed=42)
samples[:5]

array([11.31104767,  8.43326695, 12.46717752, 12.99556152,  6.91207347])

np.mean(samples), np.percentile(samples, [10, 50, 90])

(np.float64(10.817296195999955),
 array([ 7.94392525, 10.55262354, 13.99468873]))

Plot a quicklook chart

Use .plot() to inspect the distribution before putting it into a model. The plot shows the CDF with a lightly shaded PDF on a secondary axis.

delivery_days.plot(color="steelblue")

Fit from observed data

When observations are available, use .fit() instead. Here we create a small synthetic dataset and fit a normal distribution to it.

rng = np.random.default_rng(7)
observed = rng.normal(loc=10.5, scale=1.8, size=100)

fitted = dr.Normal.fit(observed, name="Observed delivery time, days")
fitted

Normal(dist_type='normal', name='Observed delivery time, days', elicitation_params=None, params={'mu': 10.188726010859352, 'sigma': 1.5755005786505731})

fitted.params

{'mu': 10.188726010859352, 'sigma': 1.5755005786505731}

You can use fitted distributions the same way as elicited distributions: plot them and sample from them in a Monte Carlo model.

fitted.plot(color="darkorange")

fitted.sample(size=5, seed=123)

array([ 8.63036475,  9.60927793, 12.21785301, 10.49433282, 11.63855033])