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Goodness-of-fit tests for the one-sided Lévy distribution based on quantile conditional moments.

Kewin Pączek1, Damian Jelito1, Marcin Pitera1

  • 1Institute of Mathematics, Jagiellonian University, Kraków, Poland.

Journal of Applied Statistics
|November 7, 2024
PubMed
Summary

This study introduces a new statistical method using conditional moments for testing one-sided Lévy distributions. This approach offers an effective alternative for goodness-of-fit analysis in statistical modeling.

Keywords:
60E0762F0362F0562P35estimationgoodness-of-fit testingone-sided Lévy distributionquantile conditional meanquantile conditional varianceα-stable distribution

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Area of Science:

  • Statistics
  • Probability Theory
  • Financial Mathematics

Background:

  • Goodness-of-fit testing is crucial for validating statistical models.
  • One-sided Lévy distributions are important in various fields, including finance.
  • Existing methods for these distributions have limitations.

Purpose of the Study:

  • To introduce a novel statistical framework for goodness-of-fit testing of one-sided Lévy distributions.
  • To extend previous work on quantile-based statistical analysis.
  • To provide an effective and verifiable alternative to existing methods.

Main Methods:

  • Development of a statistical framework based on the first two quantile conditional moments.
  • Extension of the scale-ratio framework using conditional variance ratios.
  • Derivation of asymptotic distributions for the proposed test statistics.

Main Results:

  • The proposed conditional moment-based statistics are effective for goodness-of-fit testing.
  • The framework extends previous findings for alpha-stable distributions.
  • Empirical power studies demonstrate the usefulness of the approach.

Conclusions:

  • The novel framework provides a valuable tool for analyzing one-sided Lévy distributions.
  • The method is shown to be a good alternative to existing techniques.
  • The framework is applicable to real-world data analysis.