[SciPy-User] How to fit parameters of beta distribution?

[John Reid]

On 24/06/11 13:58, josef.pktd at gmail.com wrote:
> On Fri, Jun 24, 2011 at 8:37 AM, John Reid<j.reid at mail.cryst.bbk.ac.uk>  wrote:
>> Thanks for the information. Just out of interest, this is what I get on
>> scipy 0.7 (no warnings)
>>
>> In [1]: import scipy.stats
>>
>> In [2]: scipy.stats.beta.fit([.5])
>> Out[2]:
>> array([  1.87795851e+00,   1.81444871e-01,   2.39026963e-04,
>>           4.99760973e-01])
>>
>> In [3]: scipy.__version__
>> Out[3]: '0.7.0'
>>
>> Also I have (following your advice):
>>
>> In [7]: scipy.stats.beta.fit([.5], floc=0., fscale=1.)
>> Out[7]:
>> array([  1.87795851e+00,   1.81444871e-01,   2.39026963e-04,
>>           4.99760973e-01])
>>
>> which just seems wrong, surely the loc and scale in the output should be
>> what I specified in the arguments? In any case from your example, it
>> seems like it is fixed in 0.9
>
> floc an fscale where added in scipy 0.9, extra keywords on 0.7 were just ignored

OK

>
>>
>> I'm assuming fit() does a ML estimate of the parameters which I think is
>> fine to do for a beta distribution and one data point.
>
> You need at least as many observations as parameters, and without
> enough observations the estimate will be very noisy. With fewer
> observations than parameters, you cannot identify the parameters.

I'm not quite sure what you mean by "identify". It is a ML estimate 
isn't it? That seems legitimate here but it wasn't really my original 
question. I was just using [.5] as an example.

Thanks,
John.