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A tale of two stations: a note on rejecting the Gumbel distribution

Rydén Jesper

Acta Geophysica

2023

Vol. 71, no. 1

385--390

The existence of an upper limit for extremes of quantities in the earth sciences, e.g. for river discharge or wind speed, is sometimes suggested. Estimated parameters in extreme-value distributions can assist in interpreting the behaviour of the system. Using simulation, this study investigated how sample size influences the results of statistical tests and related interpretations. Commonly used estimation techniques (maximum likelihood and probability-weighted moments) were employed in a case study; the results were applied in judging time series of annual maximum river flow from two stations on the same river, but with different lengths of observation records. The results revealed that sample size is crucial for determining the existence of an upper bound.

A note on analysis of extreme minimum temperatures with the GAMLSS framework

Rydén Jesper

Acta Geophysica

2019

Vol. 67, no. 6

1599--1604

Estimation of return levels, based on extreme value distributions, is of importance in the earth and environmental sciences. To incorporate non-stationarity in the modelling, the statistical framework of generalised additive models for location, scale and shape is an option, providing flexibility and with a wide range of distributions implemented. With a large set of selections possible, model choice is an issue. As a case study, we investigate annual minimum temperatures from measurements at a location in northern Sweden. For practical work, it turns out that care must be taken in examining the obtained distributions, not solely relying on information criteria. A simulation study illustrates the findings.