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Higher-order representation of Karamata theorem

Author

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  • Xi Yang
  • Qian Xiong
  • Zuoxiang Peng

Abstract

As an important result in extreme value theory, Karamata theorem provides the integral properties of regularly varying functions. In this paper, the third-order version of Karamata theorem is derived, which is generalization for the known Karamata theorem. Furthermore, analytic expressions for the second and third-order regularly varying function are established.

Suggested Citation

  • Xi Yang & Qian Xiong & Zuoxiang Peng, 2024. "Higher-order representation of Karamata theorem," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(8), pages 2744-2756, April.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:8:p:2744-2756
    DOI: 10.1080/03610926.2022.2148473
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