Addressing a Problem?

Per "A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis":

However, a relatively newer, uncommon but effective estimation method exists, namely the maximum product of spacing (MPS). It is a useful method for estimating the parameters of a distribution especially when dealing with small samples. The results of Wong and Li21and Soukissian and Tsalis22 showed that the method of MPS exhibits more stability relative to maximum likelihood and probability-weighted moments (PWM) for the Generalized Extreme Value Distribution. Asquith et al.23 demonstrated a close similarity between the quantile estimates derived from MPS and L-moments in the context of PE3 distribution. Another study by Khan et al.24 illustrated similar findings, indicating that for the intermediate size of samples, the MPS method has better reliability in comparison to L-moments.

In scipy, this method is called MSE, and is available in scipy.stats.fit, but not in scipy.stats.rv_continous.fit (and other dist objects)

Potential Solution

Add MSE / MPS to xclim.indices.stats.fit, using the scipy fit function.

Additional context

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