Analysis of sampling variability of the Standardized Precipitation Index

The Standardized Precipitation Index (SPI) is a widely used index for drought monitoring purposes that requires the preliminary fitting of a probability distribution to monthly precipitation aggregated at different time scales. The sampling properties of the SPI are investigated as a function of the sample size adopted for such distribution fitting. In particular, sampling properties of SPI, such as bias and mean square error (MSE), are analytically derived assuming the underlying precipitation series normally distributed, and compared with numerical values obtained by simulation for the cases of gamma and lognormal distributions. Also, the probabilities of correctly or incorrectly classifying drought conditions through the SPI are computed as a function of the available sample size. Results indicate that SPI values are significantly affected by the size of the sample adopted for its estimation. Furthermore, the theoretical MSE computed for the normal case fits well the one obtained numerically in the case of gamma and log-normal distributions, and therefore can find general application to estimate approximate confidence intervals for SPI values.