Use of Gamma distribution for SPEI calculations

[s-m-t-c]

I was just re-reading the key paper on SPEI¹ and noted the authors statement:

"Although the SPI can be calculated using a two-parameter distribution, such as the gamma distribution, a three-parameter distribution is needed to calculate the SPEI. In two-parameter distributions, the variable x has a lower boundary of zero (0>x<∞), whereas in three-parameter distributions,, x can take values in the range (y>x<∞), where y is the parameter of origin of the distribution; consequently, x can have negative values, which are common in D series."

D here refers to the difference in D_i = P_i - PET_i

Building on this their R package² implements the gamma distribution as default for the SPI but uses a log-logistic distribution for SPEI.

I've been using the gamma distribution in climate_indices for my SPEI calculations but their paper indicates that two-parameter distributions such as this shouldn't be implemented for the SPEI. Comparisons of my results using both Gamma and Pearson III distributions show pretty negligible differences between the two

Do you have any thoughts on this?

Thanks in advance for your time and maintenance on this package!

¹Vicente-Serrano, S. M., S. Beguería, et al. (2009). "A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index." Journal of Climate 23(7): 1696-1718.

²https://cran.r-project.org/web/packages/SPEI/SPEI.pdf

[monocongo]

This is an open issue, #106. Any assistance implementing this approach would be very helpful. Can we maybe put together a short summary of the math involved before focusing on the implementation? Thanks in advance for any help with this issue!

[monocongo]

Closing since this is a duplicate of issue #106.