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Imitated student’s t distribution: a Bayesian approach

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  • Łukasz Lenart

    (Krakow University of Economics)

  • Justyna Mokrzycka-Gajda

    (Krakow University of Economics)

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.

Suggested Citation

  • Łukasz Lenart & Justyna Mokrzycka-Gajda, 2025. "Imitated student’s t distribution: a Bayesian approach," Statistical Papers, Springer, vol. 66(4), pages 1-44, June.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:4:d:10.1007_s00362-025-01720-y
    DOI: 10.1007/s00362-025-01720-y
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