Refining the central limit theorem approximation via extreme value theory

Research output: Contribution to journalArticle

Abstract

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the sum of the smaller summands. If the tail is well approximated by a Pareto density, then this new approximation has substantially smaller error rates compared to the usual normal approximation for underlying distributions with finite variance and less than three moments. It can also provide an accurate approximation for some infinite variance distributions.

Original languageEnglish (US)
Article number108564
JournalStatistics and Probability Letters
Volume155
DOIs
StatePublished - Dec 1 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Refining the central limit theorem approximation via extreme value theory'. Together they form a unique fingerprint.

  • Cite this