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

josef.pktd at gmail.com josef.pktd at gmail.com
Thu Aug 24 13:24:44 EDT 2017

```On Thu, Aug 24, 2017 at 12:57 PM, <josef.pktd at gmail.com> wrote:

>
>
> 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:
>>
>>> The latest version of numpy is 1.13.
>>>
>>> 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.)
>

Based on what I start to remember:
The power function distribution can have increasing pdf. Because of the
truncation it does not need the same parameter restriction as the power law
distribution in order to integrate to a finite value so it can be
normalized to a proper distribution.

Josef

>
> Josef
>
>
>
>
>
>>
>>
>>
>>
>>>
>>> On Thu, Aug 24, 2017 at 9:41 AM, Renato Fabbri <renato.fabbri at gmail.com>
>>> wrote:
>>>
>>>> Thanks for the reply.
>>>>
>>>> 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.r
>>>>> andom.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
>>>>> _______________________________________________
>>>>> NumPy-Discussion mailing list
>>>>> NumPy-Discussion at python.org
>>>>> https://mail.python.org/mailman/listinfo/numpy-discussion
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Renato Fabbri
>>>> GNU/Linux User #479299
>>>> labmacambira.sourceforge.net
>>>>
>>>> _______________________________________________
>>>> NumPy-Discussion mailing list
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>>>> https://mail.python.org/mailman/listinfo/numpy-discussion
>>>>
>>>>
>>>
>>> _______________________________________________
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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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