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Goodness-of-fit test for the one-sided Lévy distribution.

Aditi Kumari1, Deepesh Bhati1

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

Journal of Applied Statistics
|July 29, 2024
PubMed
Summary

A new goodness-of-fit test for the one-sided Lévy distribution was developed using a scale-ratio approach. This method compares two scale parameter estimators, proving effective in simulations and real-world data analysis.

Keywords:
62E2062F03Asymptotic normalityMonte Carlo simulationgamma distributionone-sided Lévy distribution

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • The one-sided Lévy distribution is a key probability distribution in various scientific fields.
  • Assessing the fit of this distribution is crucial for accurate data modeling.

Purpose of the Study:

  • To introduce a novel goodness-of-fit test specifically designed for the one-sided Lévy distribution.
  • To provide a robust statistical tool for verifying model assumptions.

Main Methods:

  • Development of a new test statistic based on the scale-ratio approach.
  • Confrontation of two distinct estimators for the scale parameter of the one-sided Lévy distribution.
  • Derivation of the asymptotic distribution of the test statistic under the null hypothesis.

Main Results:

  • The proposed goodness-of-fit test demonstrates reliable performance.
  • Simulations show the test's effectiveness across various known distributions.
  • Analysis of two real-world datasets validates the practical applicability of the test.

Conclusions:

  • The new scale-ratio based test offers a valuable addition to statistical inference for the one-sided Lévy distribution.
  • The test is suitable for both simulated and empirical data analysis.