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This type of simple encoding of probability distributions is used commonly in algorithms, among other things, but I don't know what to call it:

If you have a set of outcomes:

$X = \{x_1, x_2, x_3, ... x_n\}$

And associate a non-negative value (in my mind, "weight") with each outcome (assuming integers for simplicity)

$W(X) = \{x_1 \rightarrow 1, x_2 \rightarrow 3, x_3 \rightarrow 2, ... x_n \rightarrow 5\}$

Then you have a total weight

$Total(W) = \sum_{x \in X}W(x)$

And you can then assign a probability to each outcome using its own weight and the total weight:

$p(x) = \frac{W(x)}{Total(W)}$

Tim Atkinson
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1 Answers1

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This is a categorical distribution.

Michael Lugo
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  • I believe the main element of the question is defining a probability distribution using arbitrary positive weights that can sum up to any value rather than a probability mass function that sums up to 1. I don't see where this is mentioned in the Wikipedia article. – Evgeny Makarov May 13 '20 at 17:42