Éric Dupuis

The method "APP" is an approximation. In the case of the gamma distribution, it's based on an approximation of the maximum likelihood formulation of the gamma parameters, see [eq.22 here](https://journals.ametsoc.org/view/journals/mwre/86/4/1520-0493_1958_086_0117_anotgd_2_0_co_2.xml?tab_body=pdf)

The issue in https://github.com/pydata/xarray/issues/2511 was solved, but there remains an error. For instance, ```python import xarray as xr import numpy as np import xclim snw = xr.tutorial.load_dataset("air_temperature").air snw.attrs["units"] = "kg...

I'm pretty much done here I think, but I would like to test a bit more situations where we have negative values. I need to find realistic cases, not too...

So I tried to obtain a proper estimation of `loc` parameter in the case of the gamma distribution, resorting to approximations as it's already the case when we have the...

I will implement a very rudimentary estimation of the `loc` parameter using the quantiles: Consider an ordered time series $X_1, X_2, \dots, X_n$. The rawest approximation would be: $\text{loc}^* =...

I had to change some results in test_indices. The most significant changes are for the fisk distribution since I changed significantly the approximations. We now have a more rigorous implementation...

I've been exploring the sensitivity to initial guesses in our procedure. Consider what is done in `test_indices.py` (`test_standardized_precipitation_index`, etc), computing a few values of SPI/SPEI. I show the example with...

I did the computation for 20 values of loc0 between 0 and the guess I outlined above. There is some variability in the spi output, and that's true for any...

A bit of a tangent, but I was wondering how does this compare to the error in a single fit. I generate 30 points in a gamma dist with R,...

I've been battling with R trying to obtain a confirmation through another package that indeed, MLE is difficult for 3-parameters function. I've had good success working with 2-params distributions that...