Chi-square-type distributions for heavy-tailed variates

Stefan Mittnik; Svetlozar T. Rachev; Jeong Ryeol Kim

doi:10.1017/s0266466698143037

Chi-square-type distributions for heavy-tailed variates

Stefan Mittnik, Svetlozar T. Rachev, Jeong Ryeol Kim

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.

Original language	English
Pages (from-to)	339-354
Number of pages	16
Journal	Econometric Theory
Volume	14
Issue number	3
DOIs	https://doi.org/10.1017/s0266466698143037
State	Published - 1998

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title = "Chi-square-type distributions for heavy-tailed variates",

abstract = "The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.",

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AB - The distribution of sums of squared random variables with heavy-tailed distributions is investigated. Considering random variables in the domain of attraction of a stable Paretian law we derive the limiting distribution as the degrees of freedom approach infinity. The finite-degrees-of-freedom behavior for stable Paretian variates is simulated. Response surface techniques are employed to compactly summarize the simulation results for a relevant range of significance levels.

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