# [SciPy-User] Rician distributions lacks sigma parameter

josef.pktd@gmai... josef.pktd@gmai...
Wed Apr 4 12:59:39 CDT 2012

```On Wed, Apr 4, 2012 at 1:53 PM,  <josef.pktd@gmail.com> wrote:
> On Wed, Apr 4, 2012 at 1:33 PM, Morten Kjeldgaard <mok@bioxray.dk> wrote:
>> Thanks for replies Josef and Warren!
>>
>> I think my current limitation is that I don't fully grasp how the
>> shape and scale parameters are propagated to the individual stats
>> distributions, and alas the autogenerated documentation isn't always
>>
>>> Given the parameters nu and sigma (as shown in the wikipedia
>>> article), you use scipy.stats.rice by setting the scale=sigma and
>>> the shape parameter b=nu/sigma.  You can use the following script to
>>> verify this:
>>
>> Like you write, the script works fine with parameters (nu, sigma) =
>> (3.45, 0.35), but it actually fails when I try to reproduce the plots
>> in the wikipedia article. When setting (nu, sigma) = (0, 1), I get the
>> following:
>
> the shape parameter nu has to be strictly positive, eg. nu=1e-10 works
> there is a problem with the calculation for nu equal to zero

But the _pdf doesn't have a problem
>>> stats.rice._pdf(np.linspace(0,4,11),0.)
array([ 0.        ,  0.36924654,  0.58091923,  0.58410271,  0.44485968,
0.27067057,  0.13472343,  0.05555507,  0.01912327,  0.00552172,
0.00134185])

>>> stats.rice.pdf(np.linspace(0,4,11),0.)
array([ nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan])
>>>

so it should be possible to fix it for the nu=0 case, (define a>= 0 ?)

Josef

>
> Josef
>
>>
>> AssertionError:
>> Not equal to tolerance rtol=1e-07, atol=0
>>
>> x and y nan location mismatch:
>>  x: array([  0.00000000e+00,   3.99680128e-02,   7.97444092e-02,
>>          1.19139103e-01,   1.57965051e-01,   1.96039735e-01,
>>          2.33186584e-01,   2.69236346e-01,   3.04028363e-01,...
>>  y: array([ nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,
>> nan,  nan,
>>         nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,
>> nan,
>>         nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,
>> nan,...
>>
>> In other words, your defined function rice_pdf works, but stats.rice
>> does not.
>>
>> Cheers,
>> Morten
>>
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```