Like some biodiversity indices that account for species evenness (whether it is dominated by a few species), I am wondering do meteorologists use an index to describe how even a temporal rainfall distribution is? (whether most precipitation are dominated by just a few days over a long time span). Thank you.
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Try to read something about Köppen climate classification. This classification among other things tries to distinguish between rainy and dry season for many areas. So, scientist needs to know the distribution of precipitation. Another possibility could be indices described in this scientific article on the ResearchGate.
