Tim Peters <t...@python.org> added the comment:

That text is fine, if you feel something needs to be said at all. I really 
don't. A Pareto distribution of this kind with parameter <= 1.0 has infinite 
expected value - VERY long tail. Anyone who knows what they're doing already 
knows that. The reason the implementation can't "blow up" for parameters >= 
(roughly) 0.1 isn't that IEEE doubles have such a large dynamic range but 
rather that they can't represent a number < 1.0 larger than 1 - 2**-53 (so u = 
1 - random.random() is always at least 2**-53). The actual distribution has 
infinite expected value nonetheless, but the implementation is incapable of 
generating any of its very large values (which, while very rare, are also very 
large).

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Python tracker <rep...@bugs.python.org>
<https://bugs.python.org/issue41421>
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