Imitated student’s t distribution: a Bayesian approach

Łukasz Lenart () and Justyna Mokrzycka-Gajda ()
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Łukasz Lenart: Krakow University of Economics
Justyna Mokrzycka-Gajda: Krakow University of Economics

Statistical Papers, 2025, vol. 66, issue 4, No 28, 44 pages

Abstract: Abstract 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.

Keywords: Heavy-tailed distribution; Finite moments; MCMC sampler; Time series; Outliers (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01720-y

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