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Key Features

🚀 State-of-the-Art Statistical Modeling

• Designed for axial data on high-dimensional spheres.
• Fit mixtures of Watson distributions with ease using an optimized Expectation-Maximization (EM) algorithm.

🧠 Built on Rigorous Mathematics

• Powered by theoretical work on bounds for Kummer’s function and its derivatives:
  • Sablica & Hornik (2022): "On bounds for Kummer’s function ratio".
  • Sablica & Hornik (2024): "Family of integrable bounds for the logarithmic derivative of Kummer’s function".

⚡ Speed

• Heavy lifting implemented in C++ using Armadillo, delivering unmatched computational performance.
• Efficient handling of sparse matrices and large-scale data.

📊 Advanced Statistical Features

• Supports custom initialization and dynamic elimination of small clusters.
• Automated selection of optimal rejection sampling algorithms based on parameters.

📖 Comprehensive Documentation

• Full documentation and examples are available, with the package paper under review in the Journal of Statistical Computing.

Project Overview

watson is the go-to R package for modeling and analyzing axial data using the Watson distribution. It provides researchers, data scientists, and statisticians with the tools needed to:

• Simulate data from Watson distributions and their mixtures.
• Fit complex models to high-dimensional axial data.
• Accurately estimate parameters using robust numerical methods.

Why Axial Data?

Axial data are unit vectors on a sphere where directions are indistinguishable (e.g., $x$ and $-x$ are equivalent). These data arise naturally in fields such as:

• Structural Geology: Modeling rock magnetism or fault planes.
• Biostatistics: Analyzing molecular orientations.
• Machine Learning: Embedding spaces and sentiment analysis.

With watson, you can unlock the full potential of axial data, leveraging a framework that combines theoretical results with computational power.

Installation

The package is available on CRAN:

install.packages("watson")

Citation

If you use watson in your research, please cite:

@article{watson2025,
  title = "{watson: An {R} Package for Fitting Mixtures of {Watson} Distributions}",
  author = {Lukas Sablica and Kurt Hornik and Josef Leydold},
  journal = {Journal of Statistical Software},
  year = 2026,
  volume = 115,
  number = 4,
  pages  = {1--30},
  url = {https://www.jstatsoft.org/index.php/jss/article/view/v115i04},
  doi = {10.18637/jss.v115.i04}
}

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