Lp-quantiles belong to the class of generalised quantiles. In this contribution we show that the Lp-quantiles represent an important class of risk measures; we study their mathematical properties and provide some recursive equations to compute them. For the special case of the L2-quantile, also known as expectile, it has been showed the equivalence of the quantile and the expectile for a class of distributions that includes the Student-t with 2 degrees of freedom.We extend this result and show that for a general Student-t distribution with p degrees of freedom (and any affine transformation), the Lp-quantile and the quantile coincide. This result opens up new research directions for the computation of the t-quantile that is generally not available in closed form and difficult to compute
On the Lp-quantiles and the Student-t distribution / Bernardi, M.; Bignozzi, V.; Petrella, Lea. - STAMPA. - (2016), pp. 1-4. (Intervento presentato al convegno 48th scientific meeting of the Italian Statistical Society -SIS: Innovazione & Società, Metodi Statistici per la valutazione tenutosi a Università degli Studi di Salerno - Campus universitario di Fisciano).
On the Lp-quantiles and the Student-t distribution
PETRELLA, Lea
2016
Abstract
Lp-quantiles belong to the class of generalised quantiles. In this contribution we show that the Lp-quantiles represent an important class of risk measures; we study their mathematical properties and provide some recursive equations to compute them. For the special case of the L2-quantile, also known as expectile, it has been showed the equivalence of the quantile and the expectile for a class of distributions that includes the Student-t with 2 degrees of freedom.We extend this result and show that for a general Student-t distribution with p degrees of freedom (and any affine transformation), the Lp-quantile and the quantile coincide. This result opens up new research directions for the computation of the t-quantile that is generally not available in closed form and difficult to compute| File | Dimensione | Formato | |
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