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On the Lp-quantiles for the Student t distribution

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  • Bernardi, Mauro
  • Bignozzi, Valeria
  • Petrella, Lea

Abstract

Lp-quantiles are a class of generalised quantiles defined as the minimisers of an expected asymmetric power function. For p=1 and p=2 they correspond respectively to the quantiles and the expectiles. In this contribution we show that for the class of Student t distributions with p degrees of freedom, the Lp-quantile and the quantile coincide for any confidence level τ∈(0,1). The proof involves concepts from combinatorial analysis as well as a recursive formula for the truncated moments of the Student t distribution. This work extends the contribution of Koenker (1993) that shows a similar result for the expectiles.

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  • Bernardi, Mauro & Bignozzi, Valeria & Petrella, Lea, 2017. "On the Lp-quantiles for the Student t distribution," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 77-83.
    • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:77-83
    DOI: 10.1016/j.spl.2017.04.017
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    References listed on IDEAS

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    Cited by:

    1. Bignozzi, Valeria & Merlo, Luca & Petrella, Lea, 2024. "Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 44-50.
    2. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    3. Valeria Bignozzi & Luca Merlo & Lea Petrella, 2022. "Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles," Papers 2209.12855, arXiv.org.

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