Limits and Inferences for Alpha-Stable Variables-Juniper Publishers-Biostatistics and Biometrics Open Access Journal

JUNIPER PUBLISHERS-Biostatistics and Biometrics Open Access Journal

Limits and Inferences for Alpha-Stable Variables

Authored by DR Jensen

Distributions having excessive tails are modeled in various venues via a-stable sequences deficit in moments of various orders. Essential statistics are examined under independent vs spherically dependent cases. The former exhibits such critical pathologies as inconsistent sample means. The latter support versions of some classical procedures even without moments as conventionally required. In particular, despite heavy tails, Student's tests for means nonetheless remain exact in level and power. etc. AMS Subject Classification: 62E15, 62H15, 62J20. Classical statistics rest heavily on means, variances, correlations, skewness and kurtosis, requiring moments to fourth order. To the contrary, probability distributions having excessive tails, often void of first or second moments, arise in a variety of circumstances. These encompass radar tracking, image processing, acoustics, risk management, portfolios in finance, biometrics, and other venues. Supporting references include Bonato & Matteo, Cheng & Rachev, Kim et al., Kuruoglu & Zerubia, Qiou et al., Tsionas & Efthymios. Salient monographs are Arce, Chernobai & Rachev, Ibragimov et al. and Samorodnitsky & Taqqu. In these settings the classical foundations accordingly must be reworked.

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