Statistical studies of the Beta Gumbel distribution: estimation of extreme levels of precipitation

Abstract

Generalisations of common families of distributions are of interest in their own right as well as for applications. A Beta Gumbel distribution has earlier been introduced as a generalisation of the Gumbel distribution, suggesting that this would provide a more flexible tail behaviour compared to the Gumbel distribution. Through simulation studies,
the distributions are here compared closer, e.g. with respect to estimation of quantiles. Moreover, real data in the form of extreme rainfall are analysed and assessment is made
whether the proposed Beta Gumbel distribution can be superior to the standard distributions with respect to modelling tail behaviour. Estimates of return values corresponding
to return periods of lengths from 100 up to 100 000 years are found, as well as the related confidence intervals. The distribution considered does indeed provide more flexibility, but
to the price of computational issues.