New submission from David MacIver <david.maci...@gmail.com>:

The following code raises a ZeroDivisionError:


from random import Random

Random(14064741636871487939).paretovariate(0.01)


This raises:

random.py, line 692, in paretovariate
    return 1.0 / u ** (1.0/alpha)
ZeroDivisionError: float division by zero


That specific stack trace is from 3.8.5 but I've tried this on 3.6 and 3.7 as 
well.

It's a little hard to tell what the intended correct range of parameter values 
is for paretovariate, and this may just be lack of validation for the alpha < 1 
case - perhaps that was never intended to be supported?

Based on some very informal inspection, what seems to happen is that the 
probability of getting a ZeroDivisionError approaches one as you approach zero. 
They rarely occur at this level of alpha (0.01), but for alpha=0.001 they seem 
to occur just under half the time, and for alpha=0.0001 they occur more than 
90% of the time.

(For the interested, this bug was found by Hypothesis as part of its own 
testing of our integration with the Random API)

----------
components: Library (Lib)
messages: 374516
nosy: David MacIver
priority: normal
severity: normal
status: open
title: Random.paretovariate sometimes raises ZeroDivisionError for small alpha
versions: Python 3.6, Python 3.7, Python 3.8

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