On the Lp-quantiles for the Student t distribution
Abstract
L_p-quantiles represent an important class of generalised quantiles and are defined as the minimisers of an expected asymmetric power function, see Chen (1996). For p=1 and p=2 they correspond respectively to the quantiles and the expectiles. In his paper Koenker (1993) showed that the tau quantile and the tau expectile coincide for every tau in (0,1) for a class of rescaled Student t distributions with two degrees of freedom. Here, we extend this result proving that for the Student t distribution with p degrees of freedom, the tau quantile and the tau L_p-quantile coincide for every tau in (0,1) and the same holds for any affine transformation. Furthermore, we investigate the properties of L_p-quantiles and provide recursive equations for the truncated moments of the Student t distribution.
Cite
@article{arxiv.1605.07947,
title = {On the Lp-quantiles for the Student t distribution},
author = {Mauro Bernardi and Valeria Bignozzi and Lea Petrella},
journal= {arXiv preprint arXiv:1605.07947},
year = {2016}
}