Bias and variance of quantile estimates from a partial duration series

Partial duration series methods have been used to estimate the T-year event Z_T of a hydrological variable. In this paper the maximum likelihood estimate of Z_T is considered for the model with a Poisson number of peaks and independently, exponentially distributed peak magnitudes. The mean and the variance of are evaluated by finite summations. Approximations to the bias of are discussed. Although the use of a first-order asymptotic expression for var() has been criticized by earlier workers, the results from this study indicate that the error is small for the most common values of T. It is further shown that small departures from the assumed model can have a large impact on var().