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As it goes with maxims like this, it depends on the problem domain. In probability theory and statistics, a cumulative distribution function is defined as F(x) := Pr(X <= x), not Pr(X < x).

Like others are saying, it is consistency within the code base that probably matters the most.



That difference only matters for discrete probability, and has the problem that the empty interval X<0 is impossible to represent.


There are distributions that are mostly continuous but also have point-masses.


Yes, this is relevant for discrete distributions.

Why is X<0 impossible to represent? If the support is {0, 1, …, k}, then Pr(X < 0) = 1 – Pr(X >= 0) = 1 – Pr(–X <= 0) = 0.




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