Assessing significant differences between two independent samples of data is challenging when the focus is on extreme events and the distribution of data is heavy-tailed. While analysis of variance (ANOVA) is useful for assessing differences in the means, it is unsuitable for differences in tail behavior, especially when means do not exist or empirical estimation of means or higher moments is not consistent. Here, we propose an ANOVA-like decomposition to analyze tail variability, allowing for flexible representation of heavy tails through a set of user-defined extreme quantiles, possibly located outside the range of observations.

Assuming regular variation (i.e., power-laws), we introduce a test statistic to check for significant tail differences across multiple independent samples and derive its asymptotic distribution. This statistic can also be used to consistently identify a changepoint in a heavy-tailed data sequence. The changepoint is estimated as the position of the maximum of the statistic when checking for differences between the data subsets to the left and right of all changepoint candidates. The new methods are compared to competitor approaches, and we apply them to analyze tail behavior in various applications (climate model simulations ofprecipitation, and motor insurance).

Girard, S., Opitz, T., & Usseglio-Carleve, A. (2024). ANOVEX: ANalysis Of Variability for heavy-tailed EXtremes. Electronic Journal of Statistics, 18(2), 5258-5303.

Girard, S., Opitz, T., Usseglio-Carleve, A., & Yan, C. (2026+, in revision for Extremes). Changepoint identification in heavy-tailed distributions. HAL preprint https://hal.science/hal-05044135/