[SciPy-User] Rician distributions lacks sigma parameter

[josef.pktd at gmail.com]

On Wed, Apr 4, 2012 at 3:00 AM, Morten Kjeldgaard <mok at bioxray.dk> wrote:
> Hi,
>
> I am a new reader of this list, please forgive me if this issue has
> already discussed.
>
> I have been wanting to use the rician distribution (stats.rice) to
> analyze some data, but it seems that the implementation in scipy does
> not take the distribution's sigma parameter into account; rather, it
> has been set to 1.0. The wikipedia article shows the traditional
> formulation of the rician distribution [0].
>
> I understand that some distributions, e.g. stats.norm, use the scale
> parameter to define std, but this does not seem to be the case with
> stats.rice.
>
> Any ideas on how to get around this, without actually modifying
> distribution.py? I have no experience with the internals of scipy, and
> wouldn't know how to modify it correctly.
>
> Cheers,
> Morten
>
> [0] http://en.wikipedia.org/wiki/Rice_distribution

location loc and scale are handled generically for all distribution.

you can add loc=some number and scale= some number to almost all
methods of the distributions. This replaces x by (x-loc)/scale in the
calculation in the function, e.g. the _pdf, (the pdf gets an
additional 1/scale in front for the transformation)

For example:
from scipy import stats
>>> x = np.linspace(0, 10, 100)
>>> import matplotlib.pyplot as plt

>>> for s  in [0.5, 1, 2, 5, 10]: plt.plot(x, stats.rice.pdf(x, 0.5 , scale=s))
...
[<matplotlib.lines.Line2D object at 0x04EB8170>]
[<matplotlib.lines.Line2D object at 0x04EB8470>]
[<matplotlib.lines.Line2D object at 0x04EB8790>]
[<matplotlib.lines.Line2D object at 0x04EB8AB0>]
[<matplotlib.lines.Line2D object at 0x04EB8DD0>]
>>> plt.show()

However, I don't see how the rice_gen._pdf matches up with the formula
on the Wikipedia page.
It looks to me that it uses a different parameterization for the shape
 parameter v. (Or I didn't have enough coffee yet)

bugs in this case (only _pdf is defined) could be possible, because
the tests only check for consistency across methods, but in most cases
the distributions are not externally verified.

Josef


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