[SciPy-Dev] Subversion scipy.stats irregular problem with source code example
Per.Brodtkorb@f...
Per.Brodtkorb@f...
Tue Oct 12 03:17:11 CDT 2010
On Mon, Oct 11, 2010 at 4:24 PM, James Phillips <zunzun@zunzun.com> wrote:
> On Mon, Oct 11, 2010 at 10:10 AM, <josef.pktd@gmail.com> wrote:
>>
>> typo should be p4
>
> Oops - thank you.
>
>
>> If I remember correctly, you have observations that are too close to
>> the upper boundary.
>>
>> If you have an observation at the boundary, the loglikelihood is inf
>>
>> I think in these cases you have to keep the boundary of the support
>> away from the max and min of the data. Similar in other distributions,
>> as I mentioned before.
>
> Thank you.
>
>
>> If MLE doesn't work for a distribution then a global optimizer
>> wouldn't help either. In these cases, usually another estimation
>> method is recommended in the literature. For example matching
>> quantiles similar to your initial version.
>
The maximum product of spacings (MPS) method is a general method of estimating parameters in
continuous univariate distributions that in many cases solves this problem.
It is especially suited to cases where one of the parameters is an unknown
shifted origin. This occurs, for example, in the three-parameter lognormal, gamma, Generalized Extreme Value
Generalized Pareto and Weibull models.
For such distributions it is known that maximum likelihood
(ML) estimation can break down because the likelihood is unbounded and this can
lead to inconsistent estimators.
In particular MPS is shown to give consistent estimators with asymptotic efficiency
equal to ML estimators when these exist. Moreover it gives consistent, asymptoti-
cally efficient estimators in situations where ML fails.
Finally, as a by-product of the MPS, a goodness of ﬁt statistic, Moran’s statistic,
is available for evaluating the fit to the selected distribution.
Two years ago I implemented this method + some other enhancements. The source code is available here:
http://code.google.com/p/joepython/source/browse/trunk/joepython/scipystats/enhance/per/distributions_per.py
The parameters are estimated by minimizing the method nlogps in the rv_continous class.
You will find more details on the method in the following references:
Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin
R. C. H. Cheng and N. A. K. Amin
(http://links.jstor.org/sici?sici=0035-9246%281983%2945%3A3%3C394%3AEPICUD%3E2.0.CO%3B2-N)
A Note on the Estimation of Extreme Value Distributions Using Maximum Product of Spacings
T. S. T. Wong and W. K. Li
Lecture Notes-Monograph Series
Vol. 52, Time Series and Related Topics: In Memory of Ching-Zong Wei (2006), pp. 272-283
(article consists of 12 pages)
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/20461444
A Goodness-Of-Fit Test Using Moran's Statistic with Estimated Parameters
R. C. H. Cheng and M. A. Stephens
(http://links.jstor.org/sici?sici=0006-3444%28198906%2976%3A2%3C385%3AAGTUMS%3E2.0.CO%3B2-1 )
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