Ways to measure deviation from a discrete uniform distribution

Asked May 08 '22 at 20:51

Active May 09 '22 at 00:03

Viewed 212 times

I'm looking for a way to characterize the deviation from a discrete uniform distribution.

Example: 50 balls are distributed over 10 urns.

In the most equal case, all urns get 5 balls. In the most unequal case, one urn gets all balls. Is there a (scalar) statistic that measures how equal things are distributed?

I thinking of something like the Gini index, but that does not quite fit in this scenario.

edited May 08 '22 at 23:58

kjetil b halvorsen

77,844

asked May 08 '22 at 20:51

cosine

Why not just use the standard deviation? – Lynn May 08 '22 at 23:04
The discrete uniform maximizes entropy, so you can use entropy --- more generally, in ecology and other disiplines such measures are called measures of (bio)-diversity, there are many posts on this site! – kjetil b halvorsen May 08 '22 at 23:59
@cosine Start here https://en.wikipedia.org/wiki/Diversity_index – Glen_b May 09 '22 at 03:27

Ways to measure deviation from a discrete uniform distribution

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