Diverging Moments and Parameter Estimation

Abstract

Heavy tailed distributions enjoy increased popularity and become more readily applicable as the arsenal of analytical and numerical tools grows. They play key roles in modeling approaches in networking, finance, hydrology to name but a few. The tail parameter alpha is of central importance as it governs both the existence of moments of positive order and the thickness of the tails of the distribution. Some of the best known tail estimators such as Koutrouvelis and Hill are either parametric or show lack in robustness or accuracy. This paper develops a shift and scale invariant, non-parametric estimator for both, upper and lower bounds for orders with finite moments. The estimator builds on the equivalence between tail behavior and the regularity of the characteristic function of the origin and achieves its goal by deriving a simplified wavelet analysis which is particularly suited to characteristic functions.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2003
Accession Number
ADA487873

Entities

People

  • Paulo Goncalves
  • Rudolf Riedi

Organizations

  • Rice University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coefficients
  • Data Science
  • Data Sets
  • Electronic Mail
  • Estimators
  • Frequency
  • Gaussian Distributions
  • Gaussian Processes
  • Information Science
  • Integrals
  • Intervals
  • Models
  • Numerical Analysis
  • Probability Distributions
  • Random Variables
  • Statistics
  • Wavelet Transforms

Readers

  • Distributed Systems and Data Platform Development
  • Statistical inference.