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<p>The objective of this article is to develop a new symmetric distribution capable of mimicking the Student’s <i>t</i> distribution with any precision controlled by a single tuning parameter. Despite the non-existence of higher-order moments of the Student’s <i>t</i> distribution, all moments of the proposed distribution do exist. Moreover, it remains subnormal at all times, regardless of how closely it approximates the <i>t</i> distribution. We strongly advocate for Bayesian inference with the proposed distribution, given the ease of identifying observations in the tails in a formal way using latent variables. Effective MCMC methods are attainable by a specific hierarchical representation of the proposed distribution. The simulation and empirical examples demonstrate the flexibility of the proposed distribution in capturing extreme observations.</p>

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Imitated student’s t distribution: a Bayesian approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月21日

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  • Łukasz Lenart,
  • Justyna Mokrzycka-Gajda

摘要

The objective of this article is to develop a new symmetric distribution capable of mimicking the Student’s t distribution with any precision controlled by a single tuning parameter. Despite the non-existence of higher-order moments of the Student’s t distribution, all moments of the proposed distribution do exist. Moreover, it remains subnormal at all times, regardless of how closely it approximates the t distribution. We strongly advocate for Bayesian inference with the proposed distribution, given the ease of identifying observations in the tails in a formal way using latent variables. Effective MCMC methods are attainable by a specific hierarchical representation of the proposed distribution. The simulation and empirical examples demonstrate the flexibility of the proposed distribution in capturing extreme observations.