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The wrapped Rama distribution.

William Bell1, Saralees Nadarajah2

  • 1Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK.

Scientific Reports
|December 31, 2024
PubMed
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A novel one-parameter circular distribution offers simpler mathematical properties and demonstrates superior data fitting compared to existing multi-parameter models. This new wrapped distribution provides a more elementary and effective approach for analyzing circular data.

Keywords:
Circular dataMaximum likelihoodTrigonometric moments

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Area of Science:

  • Statistics
  • Probability Theory
  • Data Analysis

Background:

  • Circular data analysis often involves complex wrapped distributions.
  • Existing wrapped distributions frequently lack elementary mathematical properties.
  • This limits their practical application and interpretability in statistical modeling.

Purpose of the Study:

  • To introduce a new one-parameter wrapped distribution for circular data.
  • To demonstrate that this new distribution possesses elementary mathematical properties.
  • To compare its goodness-of-fit against established multi-parameter circular distributions.

Main Methods:

  • Development of a novel one-parameter distribution based on the wrapping technique.
  • Derivation of elementary expressions for the mathematical properties of the new distribution.
  • Comparative analysis using probability plots, density plots, AIC, and BIC on real datasets.

Main Results:

  • The proposed one-parameter distribution yields elementary expressions for all its mathematical properties.
  • It demonstrated better data fitting compared to a three-parameter distribution and six other wrapped distributions.
  • These findings were consistently observed across multiple datasets and evaluation metrics.

Conclusions:

  • The new one-parameter wrapped distribution is a mathematically tractable and statistically effective model for circular data.
  • It offers advantages over existing, more complex distributions in terms of both mathematical simplicity and fit.
  • This distribution provides a valuable new tool for researchers analyzing directional or periodic data.