The Standardized Precipitation Index (SPI) is a drought index used throughout the world which normalizes accumulated precipitation by fitting univariate probability distributions for each month or day of the year. The current approach suffers several methodological limitations, notably that time steps are fit independently, zero probability mass is estimated empirically, and non-stationarity is not explicitly considered. A novel Bayesian approach is described to address these limitations and is compared with traditional frequentist approaches using synthetic and real-world precipitation.