# The metalog distribution
This package is a Python implementation of the **metalogistic or metalog** distribution,
as described in [Keelin 2016][k2016].
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][k2016] 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](http://www.metalogdistributions.com/).
[k2016]: http://www.metalogdistributions.com/images/The_Metalog_Distributions_-_Keelin_2016.pdf
# 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](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html),
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
```python
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])
# Take random samples
my_metalog.rvs(size=10)
# These methods conveniently display useful information
my_metalog.print_summary()
my_metalog.display_plot()
```
# 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](https://tadamcz.com/). As I am currently the sole author, we can probably work something out.
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"description": "# The metalog distribution\nThis package is a Python implementation of the **metalogistic or metalog** distribution,\nas described in [Keelin 2016][k2016].\n\nThe metalog is a continuous univariate probability distribution that can be used to model data without traditional parameters.\nInstead, the distribution is parametrized by **points on a cumulative distribution function (CDF)**, and the CDF of the\nmetalog fitted to these input points usually passes through them exactly.\nThe distribution can take almost any shape.\n\nThe distribution is well suited to **eliciting full subjective probability distributions** from a few\n CDF points. If used in this way, the result is a distribution that fits these points closely, without\n imposing strong shape constraints (as would be the case if fitting to a traditional distribution like the \n normal or lognormal). [Keelin 2016][k2016] remarks that the metalog \"can be used for real-time feedback to experts\n about the implications of their probability assessments\".\n\nSee also the website [metalogdistributions.com](http://www.metalogdistributions.com/).\n\n[k2016]: http://www.metalogdistributions.com/images/The_Metalog_Distributions_-_Keelin_2016.pdf\n\n# This package\nThis package:\n* Provides an object-oriented interface to instances of the class `MetaLogistic`\n* Defines `MetaLogistic` as a subclass of SciPy [continuous distribution objects](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html),\nwhich lets us use their many convenient, performant methods.\n* Uses numerical methods to approximate a least-squares fit if the closed-form method described in Keelin 2016 fails.\n This allows us to fit an even wider range of CDF data. \n* Is fast (see `timings.py`).\n \n\n# Usage\n\n```python\nfrom metalogistic import MetaLogistic\n\nmy_metalog = MetaLogistic(cdf_xs=[-5, 2, 20], cdf_ps=[.35, .5, .95])\n\n# These methods can take scalars or arrays/lists/vectors\nmy_metalog.cdf(10)\nmy_metalog.pdf([10, 20, 21])\nmy_metalog.quantile([0.8, .99])\n\n# Take random samples\nmy_metalog.rvs(size=10)\n\n# These methods conveniently display useful information\nmy_metalog.print_summary()\nmy_metalog.display_plot()\n```\n\n# Installation \n```\npip install metalogistic\n```\n\n# Speed\n`timings.py`\n\nWhen using linear least squares:\n```\n#### Speed test ####\nData:\ncdf_ps [0.15, 0.5, 0.9]\ncdf_xs [-20, -1, 40]\nBounds: None None\n\nTimings:\n'doFit' 3.99 ms\n'createPlotData' 3.99 ms\n```\n\nWhen we are forced to use numerical fitting methods:\n```\n#### Speed test ####\nData:\ncdf_ps [0.15, 0.5, 0.9]\ncdf_xs [-20, -1, 100]\nBounds: None 1000\n\nTimings:\n'doFit' 345.08 ms\n'createPlotData' 4.98 ms\n\n#### Speed test ####\nData:\ncdf_ps [0.15, 0.5, 0.9]\ncdf_xs [-20, -1, 100]\nBounds: None None\n\nTimings:\n'doFit' 354.57 ms\n'createPlotData' 5.98 ms\n```\n\n# License\nIf AGPL is a problem for you, please [contact me](https://tadamcz.com/). As I am currently the sole author, we can probably work something out.\n",
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