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Discriminant analysis for a folded Watson distribution.

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Summary

This study introduces a folded Watson distribution for modeling directional data in the positive orthant. The Expectation-Maximization algorithm and Bayes rule are used for parameter estimation and performance evaluation.

Keywords:
62H11Directional dataEM algorithmWatson distributionfolded distributionhypersphere

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Area of Science:

  • Statistics
  • Directional Data Analysis

Background:

  • Directional data in the positive orthant require specialized distributions.
  • The Watson distribution models directional data, but not specifically for the positive orthant.

Purpose of the Study:

  • Introduce and analyze a folded Watson distribution for positive orthant directional data.
  • Develop parameter estimation methods using maximum likelihood and the Expectation-Maximization algorithm.
  • Propose and evaluate a Bayes rule for the folded Watson distribution.

Main Methods:

  • Maximum likelihood estimation via the Expectation-Maximization (EM) algorithm.
  • Simulation studies to assess parameter estimation and concentration estimator properties.
  • Bayes rule formulation and performance comparison with the Watson distribution.

Main Results:

  • The EM algorithm effectively estimates parameters for the folded Watson distribution.
  • Simulation results demonstrate the performance of the concentration estimator.
  • The proposed Bayes rule shows competitive performance compared to the Watson distribution's Bayes rule.

Conclusions:

  • The folded Watson distribution is a suitable model for directional data in the positive orthant.
  • The EM algorithm and Bayes rule provide robust estimation and decision-making tools.
  • The study offers practical applications with simulated and real-world data.