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I have a discrete probability distribution: [0.05, 0.05, 0.05, 0.25, 0.6] which represents the probability of a character(given by the index in the vector) to appear.

How can I define a measure between 0 and 1 that shows that most of the probability is concentrated on the last two characters?

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    $\begingroup$ What is the problem in working with the associated probability measure? $\mathbb P(\textrm{first 3 characters} ) = 0.05 \times 3$ and $\mathbb P(\textrm{last 2 characters} ) = 0.25 + 0.6? $ $\endgroup$ Nov 1, 2022 at 10:56
  • $\begingroup$ I wanted a function which can be applied to different probability distributions $\endgroup$
    – GIONII
    Nov 1, 2022 at 15:23
  • $\begingroup$ The writing of the question didn't apparently say so. Nevertheless, if you could find insight from another post, then all is okay at the end of the day. $\endgroup$ Nov 1, 2022 at 15:32

1 Answer 1

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What I was looking for is this: How does one measure the non-uniformity of a distribution?

Entropy is a good measure that differentiates between a uniform distribution (maximum entropy) and a 1 hot encoding (almost 0 entropy).

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