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Fredy Castellares1, Artur J Lemonte2

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Area of Science:

  • Statistics
  • Circular Data Analysis

Background:

  • The von Mises distribution is a fundamental model for circular data.
  • Limitations exist in the traditional von Mises distribution for certain data patterns.

Purpose of the Study:

  • Introduce a novel two-parameter circular family of distributions.
  • Provide a comprehensive analysis of its properties and estimation methods.

Main Methods:

  • Developed a new circular distribution family.
  • Derived general properties of the distribution.
  • Investigated maximum likelihood estimation (MLE) for model parameters.
  • Derived the expected Fisher information matrix.

Main Results:

  • A new flexible two-parameter circular distribution is proposed.
  • A straightforward numerical method for MLE is presented.
  • The expected Fisher information matrix was derived.

Conclusions:

  • The new distribution offers a valuable addition to circular statistics.
  • The proposed estimation methods facilitate practical application.
  • Empirical analysis confirms the utility of the new circular distribution.