The adequacy of the gamma distribution (GD) for monthly precipitationtotals is reconsidered. The motivation for this study is the observationthat the GD fails to represent precipitation in considerable areas ofglobal observed and simulated data.This misrepresentation may lead to erroneous estimates of theStandardised Precipitation Index (SPI), evaluations of models, andassessments of climate change.In this study, the GD is compared to the Weibull (WD), Burr Type III(BD), exponentiated Weibull (EWD) and generalised gamma (GGD) distribution.These distributions extend the GD in terms of possibleshapes (skewness and kurtosis) and the behaviour for large arguments.The comparison is based on the Akaike information criterion, whichmaximises information entropy and reveals a trade-off betweendeviation and the numbers of parameters used. We use monthly sums ofobserved and simulated precipitation for 12 calendar months of the year.Assessing observed and simulated data,(i) the Weibull type distributions give distinctly improved fitscompared to the GD and(ii) the SPI resulting from the GD overestimates(underestimates) extreme dryness (wetness).
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机译：重新考虑了伽马分布（GD）对月降水总量的适当性。这项研究的动机是观察到GD无法代表全球观测和模拟数据的相当大的区域中的降水。这种不正确的陈述可能导致对标准降水指数（SPI）的估计，模型评估和气候变化评估的错误估计。 ，将GD与Weibull（WD），Burr Type III（BD），指数Weibull（EWD）和广义伽玛（GGD）分布进行比较。这些分布在可能的形状（偏度和峰度）以及行为方面扩展了GD。比较是基于Akaike信息准则进行的，该准则最大程度地提高了信息熵，并揭示了偏差与所用参数数量之间的折衷。我们使用一年中12个日历月的每月观测和模拟降水总和。评估观测和模拟数据，（i）Weibull类型分布与GD相比拟合度显着提高;（ii）GD高估（低估）导致的SPI极度干燥（湿润）。
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