Abstract—The standardized precipitation index (SPI) is widely applied for identifying the characteristics of drought in different climatic zones around the world. The SPI calculation is commonly used two-parameter gamma probability distribution function to fit observed precipitation data, while it might not be the best distribution candidate. Selection of an improper probability may impart a bias to the SPI values, which are dependent upon a univariate probability distribution to be normalized. In arid and semi-arid environments with possible zero-precipitation months, hence, SPI calculated by two-parameters Gamma distribution probably cannot detect drought events, particularly on short times scales (1-3 months). In this study, the effects of zero precipitation on SPI values in arid and semi-arid environments of Iran are investigated, and the best candidate distribution for calculating the SPI values on different time steps (1-12 months) is recommended. To achieve such goals, different distribution functions are applied to calculated the SPI values on 1- to 12-month time scales utilizing long-term monthly precipitation records at 50 stations evenly scattered over Iran. Accordingly, different probability distribution functions in SPEI package, SCI package, and the nonparametric approach were employed for calculating the SPI values. Three statistical tests (Shapiro-Wilk, Anderson- Darling, and Kolmogorov- Smirnov) were used to determine the normality of such SPI values. From a mathematical point of view, candidate distributions were categorized into two groups: short (1-2 months) and long (>3 months) accumulation periods. Based on their ability to estimate the SPI values, nonparametric approach is recommended for long accumulation periods in arid and semi-arid environments, while the Weibull probability for short ones.

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