Extreme Value Modeling with Generalized Pareto Distributions for Rounded Data
Pub. online: 5 March 2026
Type: Methodology Article
Open Access
Open Access
Area: Spatial and Environmental Statistics
Accepted
3 February 2026
3 February 2026
Published
5 March 2026
5 March 2026
Abstract
In extreme value analysis, the impact of rounding in data, a form of quantization, on statistical inferences beyond point estimation has not been comprehensively studied. This paper addresses these challenges by considering rounded data as interval-censored. The maximum likelihood estimators of the model parameters tailored to account for interval censoring are asymptotically unbiased and efficient. Further, we adapt classic goodness-of-fit tests, such as the Anderson-Darling test, for rounded data based on the maximum likelihood estimator. The resulting tests have appropriate sizes and considerable power. One application of such tests is threshold selection for the peak over threshold approach in extreme value analysis. The efficacy of our estimation approach and the goodness-of-fit tests are demonstrated through a simulation study involving data rounded from generalized Pareto distributions. Applying this method to precipitation data from 18 stations in eastern Washington, an area with typically low precipitation and expecting a significant rounding effect, we observe narrower interval estimates of return levels.
Supplementary material
Supplementary MaterialThe Supplementary Material presented additional simulation results confirming MLE-IC’s robustness under extreme rounding conditions and extended power comparisons. It also provided supplementary precipitation data analysis across 18 eastern Washington stations, showing that MLE-IC consistently selected lower thresholds and yielded better model fit and return-level estimates than MLE-N.
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