Bias and variance reduction of high return levels for extreme hazard modelling

Abstract

AbstractMany existing extremal data span only a few decades that result in large uncertainty in the estimated shape parameter of the extreme hazard model. This in turn leads to potentially large bias and variance of extrapolated extreme values at high return levels. This paper illustrates a statistical method that helps obtain hazard models that produce estimates at high return levels with reduced bias and variance. This method makes use of the maximum recorded values of extremal data that are independently recorded from a number of observational sites or generated by heterogeneous mechanisms. The logarithmically transformed average recurrence interval of the maximum recorded value at a site is shown to follow the Gumbel (Type I extreme value) distribution; therefore, multiple, say $$m$$ m , observational sites provide a sample of size $$m$$ m log-transformed average recurrence intervals, each from a distinct site. The sample can be treated as a sample from a Gumbel distribution, irrespective of the underlying hazard-generating mechanisms or the statistical hazard models. Application of the method is illustrated by analysis of the extreme wind gust data from automatic weather stations in South Australia and shown to lead to significant reduction of 2.9 m/s in potential bias of the mean and a reduction of 98.1% in variance of the 500-year gust speed at Adelaide Airport. The results are compared to the specifications in the Australian standard AS/NZS 1170.2:2021 and indicate that the standard may have overestimated the wind gust hazard; hence, the specified design wind speeds may fall on the conservative side for South Australia.