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A paper describes how the Tweedie distribution fitting can be used for drought monitoring using streamflow data: Statistical distributions for monthly aggregations of precipitation and streamflow in drought indicator applications; Svensson, Hannaford, and Prosdocimi, 2017
This is probably best tackled by creating a function in compute.py named transform_fitted_tweedie(), along the same lines as the existing transform_fitted_gamma() and transform_fitted_pearson() functions. Then these can be used to create spi_tweedie() in the indices.py module.
Credit to Curtis Riganti for highlighting the utility of this additional fitting. Thanks!