The metalog distribution

This package is a Python implementation of the metalogistic or metalog distribution, as described in Keelin 2016.

The metalog is a continuous univariate probability distribution that can be used to model data without traditional parameters. Instead, the distribution is parametrized by points on a cumulative distribution function (CDF), and the CDF of the metalog fitted to these input points usually passes through them exactly. The distribution can take almost any shape.

The distribution is well suited to eliciting full subjective probability distributions from a few CDF points. If used in this way, the result is a distribution that fits these points closely, without imposing strong shape constraints (as would be the case if fitting to a traditional distribution like the normal or lognormal). Keelin 2016 remarks that the metalog "can be used for real-time feedback to experts about the implications of their probability assessments".

See also the website metalogdistributions.com.

This package

This package:

• Provides an object-oriented interface to instances of the class MetaLogistic
• Defines MetaLogistic as a subclass of SciPy continuous distribution objects, which lets us use their many convenient, performant methods.
• Uses numerical methods to approximate a least-squares fit if the closed-form method described in Keelin 2016 fails. This allows us to fit an even wider range of CDF data.
• Is fast (see timings.py).

Usage

from metalogistic import MetaLogistic

my_metalog = MetaLogistic(cdf_xs=[-5, 2, 20], cdf_ps=[.35, .5, .95])

# These methods can take scalars or arrays/lists/vectors
my_metalog.cdf(10)
my_metalog.pdf([10, 20, 21])
my_metalog.quantile([0.8, .99])

# These methods conveniently display useful information
my_metalog.print_summary()
my_metalog.display_plot()

See also example_usage.py

Installation

pip install metalogistic

Speed

timings.py

When using linear least squares:

#### Speed test ####
Data:
cdf_ps [0.15, 0.5, 0.9]
cdf_xs [-20, -1, 40]
Bounds: None None

Timings:
'doFit'  3.99 ms
'createPlotData'  3.99 ms

When we are forced to use numerical fitting methods:

#### Speed test ####
Data:
cdf_ps [0.15, 0.5, 0.9]
cdf_xs [-20, -1, 100]
Bounds: None 1000

Timings:
'doFit'  345.08 ms
'createPlotData'  4.98 ms

#### Speed test ####
Data:
cdf_ps [0.15, 0.5, 0.9]
cdf_xs [-20, -1, 100]
Bounds: None None

Timings:
'doFit'  354.57 ms
'createPlotData'  5.98 ms

License

If AGPL is a problem for you, please contact me. As I am currently the sole author, we can probably work something out.