2023/07/06 by Haijun Li, Li, Haijun · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2307.03316
openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Operator regular variation reveals general power-law distribution tail decay phenomena using operator scaling, that includes multivariate regular variation with scalar scaling as a special case. In this paper, we show that a multivariate Liouville distribution is operator regularly varying if its driving function is univariate regularly varying. Our method focuses on operator regular variation of multivariate densities, which implies, as we also show in this paper, operator regular variation of the multivariate distributions. This general result extends the general closure property of multivariate regular variation established by de Haan and Resnick in 1987.