The statistical treatment of flood flows

The estimation of return periods of floods is considered from the point of view of mathematical statistics. This requires, essentially, the estimation of the tail of a probability distribution from a sample of values which is usually not dense in this tail. The error in the estimation of a flood corresponding to a given probability arises from two sources: (1) the uncertainty as to the mathematical form of the distribution; (2) the uncertainty arising from the statistical errors of estimation of the parameters of the distribution which occur because of the finiteness of the length of record. These errors are illustrated on a numerical example by fitting a log‐normal distribution and a type III distribution to fifty annual values of extreme monthly flow of the River Murray.