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<p>Finite mixture models constitute a versatile framework for capturing latent heterogeneity and complex structural features in data. In many practical settings, observations deviate from normality, exhibiting skewness, heavy tails, or multimodal behaviour. Stable distributions form a rich and flexible class capable of modelling such heavy-tailed phenomena due to their ability to accommodate varying tail thickness and shape characteristics. In this work, we propose a new class of circular mixture models based on the wrapped stable distribution, which belongs to the Fourier family and admits an explicit and convergent Fourier series representation. The resulting mixture of wrapped stable (MWS) distributions provides an extended modelling framework for circular data exhibiting heterogeneous concentration and tail behaviour. Parameter estimation is carried out using the Expectation–Maximization (EM) algorithm, tailored to the wrapped stable setting. The practical relevance and modelling capacity of the proposed approach are illustrated through two real data applications involving wind direction time series and sole mark measurements.</p>

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Wrapped Stable Distribution-based Inference for Finite Mixture Models: Principles and Applications

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Smriti Sikha Sarma,
  • Bishal Gurung,
  • Bhanita Das

摘要

Finite mixture models constitute a versatile framework for capturing latent heterogeneity and complex structural features in data. In many practical settings, observations deviate from normality, exhibiting skewness, heavy tails, or multimodal behaviour. Stable distributions form a rich and flexible class capable of modelling such heavy-tailed phenomena due to their ability to accommodate varying tail thickness and shape characteristics. In this work, we propose a new class of circular mixture models based on the wrapped stable distribution, which belongs to the Fourier family and admits an explicit and convergent Fourier series representation. The resulting mixture of wrapped stable (MWS) distributions provides an extended modelling framework for circular data exhibiting heterogeneous concentration and tail behaviour. Parameter estimation is carried out using the Expectation–Maximization (EM) algorithm, tailored to the wrapped stable setting. The practical relevance and modelling capacity of the proposed approach are illustrated through two real data applications involving wind direction time series and sole mark measurements.