Standardized Index Calculation Methods

Log-logistic:

This distribution is typically used when calculating Standardized Precipitation Evapotranspiration Index (SPEI) and Evaporative Demand Drought Index (EDDI) and follows the methods outlined in Vicente-Serrano et al. 2010. Following this paper, the L-moment method was utilized to acquire the parameters for the log-logistic distribution.

The normalized drought index values are obtained by applying the inverse normal function to the log-logistic PDF following Abramowitz and Stegun (1965).

Gamma:

This distribution is typically used when calculating Standardized Precipitation Index  (SPI) and follows the methods outlined in McKee et al 1993. We use the maximum likelihood method to estimate gamma parameters. Additional reference is provided by this handout http://www.atmo.arizona.edu/students/courselinks/fall11/atmo529/Lectures/SPIhandout.pdf

The normalized drought index values are obtained by applying the inverse normal function to the gamma PDF following Abramowitz and Stegun (1965).

Non-parametric:

This distribution computes a standardized index using a non-parametric ranking approach based on the Tukey plotting positions. The normalized drought index values are obtained by applying the inverse normal function to the plotting positions PDF following Abramowitz and Stegun (1965).

Citations

Abramowitz, M. and Stegun, I.A. (Eds.) (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications Inc., New York, 1046 p.

Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of climate, 23(7), 1696-1718.

McKee, Thomas B., Nolan J. Doesken, and John Kleist. "The relationship of drought frequency and duration to time scales." Proceedings of the 8th Conference on Applied Climatology. Vol. 17. No. 22. 1993.