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On the Lp-quantiles for the Student t distribution

Mauro Bernardi, Valeria Bignozzi and Lea Petrella

Statistics & Probability Letters, 2017, vol. 128, issue C, 77-83

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.

Keywords: Generalised quantiles; Expectiles; Quantiles; Truncated moments; Student t distribution (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.04.017

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