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Following from this question, is there a way to use any method other than MLE (maximum-likelihood estimation) for fitting a continuous distribution in scipy? I think that my data may be resulting in the MLE method diverging, so I want to try using the method of moments instead, but I can't find out how to do it in scipy. Specifically, I'm expecting to find something like
scipy.stats.genextreme.fit(data, method=method_of_moments)
Does anyone know if this is possible, and if so how to do it?
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moment(array, axis=0) function calculates the nth moment about the mean for a sample i.e. array elements along the specified axis of the array (list in python). Parameters : array : Input array or object having the elements to calculate the moment. axis : Axis along which the moment is to be computed.
ppf: percent point function (or inverse cumulative distribution function) ppf returns the value x of the variable that has a given cumulative distribution probability (cdf). Thus, given the cdf(x) of a x value, ppf returns the value x itself, therefore, operating as the inverse of cdf.
The first four are: 1) The mean, which indicates the central tendency of a distribution. 2) The second moment is the variance, which indicates the width or deviation. 3) The third moment is the skewness, which indicates any asymmetric 'leaning' to either left or right.
It is useful for obtaining probabilistic distributions. SciPy Stats can generate discrete or continuous random numbers. It also consists of many other functions to generate descriptive statistical values. We can deal with random, continuos, and random variables.
Few things to mention:
1) scipy does not have support for GMM. There is some support for GMM via statsmodels (http://statsmodels.sourceforge.net/stable/gmm.html), you can also access many R routines via Rpy2 (and R is bound to have every flavour of GMM ever invented): http://rpy.sourceforge.net/rpy2/doc-2.1/html/index.html
2) Regarding stability of convergence, if this is the issue, then probably your problem is not with the objective being maximised (eg. likelihood, as opposed to a generalised moment) but with the optimiser. Gradient optimisers can be really fussy (or rather, the problems we give them are not really suited for gradient optimisation, leading to poor convergence).
If statsmodels and Rpy do not give you the routine you need, it is perhaps a good idea to write out your moment computation out verbose, and see how you can maximise it yourself - perhaps a custom-made little tool would work well for you?
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