The log Pearson type 3 distribution: The T‐year event and its asymptotic standard error by maximum likelihood theory

The maximum likelihood estimators for the three distribution parameters of a log Pearson type 3 distribution are derived from the logarithmic likelihood function and a solution method is given.The T‐year event is then derived as a function of these parameters and the standard normal deviate t. These parameters are subject to sampling variances and covariances, whereas t is not. By using the logarithmic likelihood function the inverse dispersion matrix is derived, hence the variances and covariances of the parameters. Entering these in the general variance of the estimate equation of a function of three variables leads to an estimate of the asymptotic standard error of estimate of the T‐year event. Flood data from 37 hydrometric stations on Canadian rivers were analyzed by this method and compared with the more common moment analysis. In all cases the maximum likelihood analysis is markedly superior in terms of the estimate of standard error of estimate, but the asymptotic nature of the result must always be borne in mind. Possible sources of bias in the maximum likelihood estimate of the T‐year event are discussed.