random.expovariate(lambd) should handle lambd=0 cleanly, and probably
return a FP infinity.

At the moment it gives:

ZeroDivisionError: float division

An exponential distribution with parameter 0 isn't an exponential distribution any more. On the real line, there isn't
even a limiting distribution as the parameter approaches 0.

Is there really any use for having expovariate degenerate this way?
It seems much more likely that a call to random.expovariate(0) is
caused by a bug somewhere, so should raise an exception. Which is exactly
what it does already.

The proposed change would also not be in keeping with the philosophy
behind most of Python's mathematics, which is to raise exceptions rather
than returning exceptional (nan, inf) results. (Think of it as IEEE 754
will the invalid, overflow and division-by-zero signals all being
trapped.)

I would suggest adding a note to the documentation stating clearly that
the parameter should be nonzero. The documentation is also unclear on
whether a negative parameter value is permitted, although the current code
works exactly the way that I'd expect for a negative parameter.

If a negative parameter is permitted then the last sentence of the
docstring:

"""... Returned values range from 0 to positive infinity."""

is inaccurate, since values range from 0 to negative infinity in that
case. If it's not supposed to be permitted then perhaps the docstring
should mention that the parameter should be positive?

That's all true - the only thing in favour of my suggestion is that to
allow lambda=0 is sometimes useful in simulations, meaning that it's
infinite time to the next event, i.e. it never occurs. A FP infinity
would do this without requiring a special case.

At least the documentation should state the restrictions on lambda.

to allow lambda=0 is sometimes useful in simulations, meaning that it's
infinite time to the next event, i.e. it never occurs.

Thanks; that makes sense. If 1./0. returned inf then expovariate would
already do what you want. But rightly or wrongly, Python just doesn't
work that way.

Incidentally, if expovariate had been written to take the mean as its
argument (instead of the reciprocal of the mean) then this would be easy:
just provide a parameter of float('inf') and everything would work. (And
a parameter of 0 would give a point distribution at 0, which again seems
perfectly sound.)

Doc fixes in r68378. Closing.

I concur with Mark.