A standard approach to model the extreme values of a stationary
process is the peaks over threshold method, which consists of imposing
a high threshold, identifying clusters of exceedances of this
threshold, and fitting the maximum value from each cluster using the
generalised Pareto distribution. This approach is strongly justified
by underlying asymptotic theory. We propose an alternative model for
the distribution of the cluster maxima which accounts for the
sub-asymptotic theory of extremes of a stationary process. This new
distribution is a product of two terms, one for the marginal
distribution of exceedances and the other for the dependence structure
of the exceedance values within a cluster. We illustrate the
improvement in fit, measured by the root mean square error of the
estimated quantiles, offered by the new distribution over the peaks
over thresholds analysis using simulated and hydrological data, and we
suggest a diagnostic tool to help identify when the proposed model is
likely to lead to such an improvement in fit.