https://github.com/fmind/ouroboros
Implementation of the Ouroboros index: a size-independent diversity statistic
https://github.com/fmind/ouroboros
diversity index metrics python statistics
Last synced: 19 days ago
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Implementation of the Ouroboros index: a size-independent diversity statistic
- Host: GitHub
- URL: https://github.com/fmind/ouroboros
- Owner: fmind
- License: other
- Created: 2019-03-13T15:26:41.000Z (about 6 years ago)
- Default Branch: master
- Last Pushed: 2019-07-04T08:54:24.000Z (almost 6 years ago)
- Last Synced: 2025-04-11T04:43:19.510Z (19 days ago)
- Topics: diversity, index, metrics, python, statistics
- Language: Jupyter Notebook
- Homepage:
- Size: 165 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
# What is Ouroboros ?
_Ouroboros_ is a function which measures the uniformity of a list of frequencies, independently of the size of the list.
__Input__:
* an array of frequencies (counts or proportions values)
__Output__:
* Index: quantifies the uniformity of a list in an unitless scale (0 for min. uniformity, 1 for max. uniformity)
* Indice (option): the minimal number of groups that includes at least 50\% of the individuals (between 0 and N/2)
__Interpretation__:
* Index: twice the minimum percentage of values to include in order to reach 50% of individuals
* Index/2: the minimal proportion of groups which includes 50% of individuals
__Example__:
Individuals are evenly distributed among groups: Index = 1, Indice = 3
Individuals are distributed in 1 group: Index = 0, Indice=1
# How does Ouroboros work ?
A technical implementation of the function is provided in _ouroboros.py_.
__Pseudo-code (high-level)__:
- sort the list of frequencies in descending order
- accumulate values from the head until 50% individuals are included
- smooth values depending on the final percentage of individuals accumulated
- return the Index (and optionally the Indice) of the list
# Why is Ouroboros different ?
__Compared to the [median](https://en.wikipedia.org/wiki/Median)__, _Ouroboros_
does not cut a list of values in two lists of equal sizes. Instead, the function
finds the minimal number of values to sum in order to reach 50% of the distribution.
__Compared to a
[Pearson's chi-squared test](https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test#Discrete_uniform_distribution)__,
_Ouroboros_ is not a statistic test value. Thus, _Ouroboros_ is simpler to compute and to interpret.
__Compared to
[Diversity indexes](https://en.wikipedia.org/wiki/Diversity_index)__, _Ouroboros_
returns percentage values instead of squared values (Gini-Simpson index) or
logarithmic values (Shannon index). This choice makes the function easier to
interpret since the scale is linear. In addition,
_Ouroboros_ will always returns an index of 0 or 1 for the two most extremes cases.
ARRAY | OURO | GINI
----------------|------|-----
100 | 1.00 | 0.00
100,0 | 0.00 | 0.00
75,25 | 0.50 | 0.38
60,40 | 0.80 | 0.48
50,50 | 1.00 | 0.50
100,0,0 | 0.00 | 0.00
90,5,5 | 0.15 | 0.19
67,23,10 | 0.49 | 0.49
65,35,0 | 0.52 | 0.45
50,30,20 | 0.75 | 0.62
34,33,33 | 0.99 | 0.67
100,0,0,0 | 0.00 | 0.00
80,20,0,0 | 0.20 | 0.32
60,20,10,10 | 0.40 | 0.58
40,40,10,10 | 0.70 | 0.66
49,49,1,1 | 0.52 | 0.52
30,30,20,20 | 0.90 | 0.74
25,25,25,25 | 1.00 | 0.75
100,0,0,0,0 | 0.00 | 0.00
80,20,0,0,0 | 0.17 | 0.32
50,30,10,10,0 | 0.42 | 0.64
30,25,20,20,5 | 0.71 | 0.77
25,25,25,15,10 | 0.75 | 0.78
25,20,20,20,15 | 0.96 | 0.79
20,20,20,20,20 | 1.00 | 0.80
# FAQ
### Why the name of the function is Ouroboros ?
Heads and tails of statistic distributions are characteristic elements that can be used to measure equalities.
_Ouroboros_ is the "tail-devouring snake", which describes where "the head bites the tail of a distribution".