Frequency Curves for Annual Flood Series with Some Zero Events or Incomplete Data

In fitting a theoretical frequency distribution to a set of data, a problem arises if the series contains a number of zero values, as may occur in annual flood peak data for small, arid‐region streams. The problem is twofold: first, commonly used distributions do not fit such a set of data; second, if a logarithmic transformation of the data is being used, logarithms of zero flows are not usable in a computation. To overcome the difficulties, a theorem of conditional probability is used. The probability of occurrence of a nonzero peak is combined with the conditional probability of exceeding a given flood magnitude, given that a nonzero peak has occurred. The method has been found useful also for fitting flood series in which information of peak annual floods below a specific stage is lacking.