# [Numpy-discussion] power function distribution or power-law distribution?

josef.pktd at gmail.com josef.pktd at gmail.com
Thu Aug 24 12:57:43 EDT 2017

```On Thu, Aug 24, 2017 at 10:56 AM, Renato Fabbri <renato.fabbri at gmail.com>
wrote:

> On Thu, Aug 24, 2017 at 11:47 AM, Nathan Goldbaum <nathan12343 at gmail.com>
> wrote:
>
>>
>> In this case, as described in the docs, a power function distribution is
>> one with a probability desnity function of the form ax^(a-1) for x between
>> 0 and 1.
>>
>
> ok, let's try ourselves to relate the terms.
> Would you agree that the "power function distribution" is a "power-law
> distribution"
> in which the domain is restricted to be [0,1]?
>

I would phrase it weaker. The emphasis for power-law distribution is often
or commonly on the tail behavior.

The functional form of the pdf is the same as the power-law distribution
but restricted to a finite interval [0,1]
or
The power function distribution can be considered as a truncated power-law
distribution.

(I looked at it maybe 9 years ago, but gave up on the similarity because
the purpose is very different, at least based on what I looked at at the
time. The similarity in name also got me confused initially.)

Josef

>
>
>
>
>>
>> On Thu, Aug 24, 2017 at 9:41 AM, Renato Fabbri <renato.fabbri at gmail.com>
>> wrote:
>>
>>>
>>> But the question remains:
>>> how are the terms "power function distribution"
>>> and "power-law distribution" related?
>>>
>>> The documentation link you sent have no information on this.
>>> (
>>> And seems the same as I get here
>>> In [6]: n.version.full_version
>>> Out[6]: '1.11.0'
>>> )
>>>
>>> On Thu, Aug 24, 2017 at 11:07 AM, Pauli Virtanen <pav at iki.fi> wrote:
>>>
>>>> to, 2017-08-24 kello 10:53 -0300, Renato Fabbri kirjoitti:
>>>> > numpy.random.power.__doc__
>>>> >
>>>> > uses only the term "power function distribution".
>>>>
>>>> The documentation in the most recent Numpy version seems to be more
>>>> explicit, see the Notes section for the PDF:
>>>>
>>>> https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.power
>>>> .html
>>>> <https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.power.html>
>>>>
>>>> > BTW.  how is this list related to numpy-discussion at scipy.org?
>>>>
>>>> That's the old address of this list.
>>>> The current address is numpy-discussion at python.org and it should be
>>>>
>>>> --
>>>> Pauli Virtanen
>>>> _______________________________________________
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>>>>
>>>
>>>
>>>
>>> --
>>> Renato Fabbri
>>> GNU/Linux User #479299
>>> labmacambira.sourceforge.net
>>>
>>> _______________________________________________
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>>>
>>>
>>
>> _______________________________________________
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>>
>>
>
>
> --
> Renato Fabbri
> GNU/Linux User #479299
> labmacambira.sourceforge.net
>
> _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at python.org
> https://mail.python.org/mailman/listinfo/numpy-discussion
>
>
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