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Jackknife empirical likelihood test for testing one-sided Lévy distribution.

Deepesh Bhati1, Sudheesh K Kattumannil2

  • 1Department of Statistics, Central University of Rajasthan, Ajmer, India.

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|June 16, 2022
PubMed
Summary

This study introduces a new statistical test for one-sided Lévy distributions using a jackknife empirical likelihood method. The developed tests demonstrate strong power in simulations and are applied to real-world data.

Keywords:
Jackknife empirical likelihoodLévy distributionU-empirical processWilk's theorem

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Lévy distributions are important in probability and statistics.
  • Existing methods for testing one-sided Lévy distributions may have limitations.

Purpose of the Study:

  • To develop a novel jackknife empirical likelihood-based test for one-sided Lévy distributions.
  • To create an adjusted version of the test for improved performance.

Main Methods:

  • Construction of a U-empirical process.
  • Application of jackknife empirical likelihood techniques.
  • Development of an adjusted jackknife empirical likelihood test.

Main Results:

  • The proposed tests exhibit very good statistical power against various alternatives.
  • Simulation studies confirm the effectiveness of the new tests.

Conclusions:

  • The jackknife empirical likelihood-based tests are effective for detecting one-sided Lévy distributions.
  • The methodology is illustrated with practical applications on real datasets.