For daily rainfall the normalized rainfall curve (NRC) provides a plot of the cumulative percentage of rain days (y) against the cumulative percentage of rain amount (x). It is not immediately clear whether the equations that have been widely used to represent the relationship between xand ycorrespond to a valid probability distribution for daily rainfall amounts. We show that such distributions exist, but that they are truncated, i.e. not all positive values of rainfall have non-zero probability. In practice, the truncation may not be too important, but the form of the equations relating xand yis also determined for a number of well-known probability distributions that are not truncated. The fit of the corresponding NRCs to some published rainfall data is examined.
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Jolliffe et al. (1996) studied this question.