Appropriate statistical rainfall distribution models for the computation of standardized precipitation index (SPI) in Cameroon

The performance of the Standardized Precipitation Index (SPI) is affected by the choice of an incorrect probability distribution function, which can skew the values of the index, exaggerating or minimizing the severity of drought. This study aims to test data fitability of ten statistical distribution functions (gamma, weibull, exponential, lognormal, gumbel, cauchy, logistic, chi-square, burr, pareto) for SPI computation at time scales (TSs) of 3, 6, 9, 12, 15, 18, 21 and 24 months, and to quantify the errors made if the gamma function were used by default as is the case in general. Monthly precipitation data collected at 24 meteorological stations distributed in the five Agro-Ecological Zones (AEZs) of Cameroon were used for the period 1951-2005. The parameters of the distribution functions were estimated with the Maximum Likelihood (ML) method, and the Kolmogorov-Smirnov (K-S) test was applied to assess how well these functions fit the data. The results show that the logistic and burr distributions provide for several stations of the five AEZs the best data fits. A comparative study between the SPIs from the appropriate distribution and the gamma functions shows a significant qualitative and quantitative difference in several stations and the root mean square error (RMSE) increases with the TS and with the severity of drought.