Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics

Marcin Pitera (), Aleksei Chechkin and Agnieszka Wyłomańska
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Marcin Pitera: Jagiellonian University
Aleksei Chechkin: University of Potsdam
Agnieszka Wyłomańska: Hugo Steinhaus Center, Wrocław University of Science and Technology

Statistical Methods & Applications, 2022, vol. 31, issue 2, No 15, 387-424

Abstract: Abstract The class of $$\alpha$$ α -stable distributions is ubiquitous in many areas including signal processing, finance, biology, physics, and condition monitoring. In particular, it allows efficient noise modeling and incorporates distributional properties such as asymmetry and heavy-tails. Despite the popularity of this modeling choice, most statistical goodness-of-fit tests designed for $$\alpha$$ α -stable distributions are based on a generic distance measurement methods. To be efficient, those methods require large sample sizes and often do not efficiently discriminate distributions when the corresponding $$\alpha$$ α -stable parameters are close to each other. In this paper, we propose a novel goodness-of-fit method based on quantile (trimmed) conditional variances that is designed to overcome these deficiencies and outperforms many benchmark testing procedures. The effectiveness of the proposed approach is illustrated using extensive simulation study with focus set on the symmetric case. For completeness, an empirical example linked to plasma physics is provided.

Keywords: $$\alpha$$ α -stable distribution; Heavy-tailed distribution; Conditional variance; Trimmed variance; Quantile conditional variance; Goodness-of-fit test; 62F03; 60E07; 62P35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10260-021-00571-9

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