Truncated distributions for the standardized precipitation (SPI) and standardized streamflow (SSI) indices in a tropical basin

Abstract

This study evaluated whether truncated three-parameter distributions improve the selection of candidate distributions for the Standardized Precipitation Index (SPI) and Standardized Streamflow Index (SSI). We compared their performance with two-parameter distributions across time scales of 1 to 12 months in a tropical basin. Nine probability distributions were assessed using a multi-criteria approach based on the Lilliefors goodness-of-fit test, Akaike information criterion, Shapiro-Wilk normality test, and deviation from normality. Truncated distributions improved the comparison between two- and three-parameter distributions regarding their ability to generate normally distributed index estimates. The truncated Pearson-III and truncated generalized extreme value distributions emerged as the most suitable distributions for estimating the SPI and SSI, respectively, in a tropical basin. Considering that the Tweedie distribution ranked as the second-best distribution for calculating both indices, it emerged as an appropriate choice for using a single model to calculate both the SPI and SSI in such regions.