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Add unit tests for Gini coefficient for uniform and exponential distribution of values. [CI SKIP]

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Nick Thompson
2018-12-16 23:05:00 -07:00
parent efdafa2643
commit cee62a833c
4 changed files with 129 additions and 65 deletions
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doc/vector_functionals/univariate_statistics.qbk
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@@ -149,13 +149,15 @@ Compute the Gini coefficient of a dataset:
/Nota bene: The input data is altered-in particular, it is sorted./
/Nota bene:/ Different authors use different conventions regarding the overall scale of the Gini coefficient.
We have chosen to follow [@https://arxiv.org/pdf/0811.4706.pdf Hurley and Rickard's definition], which [@https://en.wikipedia.org/wiki/Gini_coefficient Wikipedia] calls a "sample Gini coefficient".
Hurley and Rickard's definition places the Gini coefficient in the range [0,1]; Wikipedia's population Gini coefficient is in the range [0, 1 - 1/ /n/].
If you wish to convert the Boost Gini coefficient to the population Gini coefficient, multiply by (/n/-1)/ /n/.
We use [@https://en.wikipedia.org/wiki/Gini_coefficient Wikipedia's] "sample Gini coefficient".
The sample Gini coefficient lies in the range [0,1], whereas the population Gini coefficient is in the range [0, 1 - 1/ /n/].
If you wish to convert the sample Gini coefficient returned by Boost to the population Gini coefficient, multiply by (/n/-1)/ /n/.
/Nota bene:/ There is essentially no reason to pass negative values to the Gini coefficient function.
However, a single use case (measuring wealth inequality when some people have negative wealth) exists, so we do not throw an exception when negative values are encountered.
You should have /very/ good cause to pass negative values to the Gini coefficient calculator.
Another use case is found in signal processing, but the sorting is by magnitude and hence has a different implementation.
See `absolute_gini_coefficient` for details.
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