# 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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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:stapro:v:128:y:2017:i:c:p:77-83

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**DOI:** 10.1016/j.spl.2017.04.017

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