Interorder relations between moments of a Student $t$ distribution, with an application to $L_p$quantiles
Abstract
This paper introduces interorder formulas for partial and complete moments of a Student $t$ distribution with $n$ degrees of freedom. We show how the partial moment of order $n  j$ about any real value $m$ can be expressed in terms of the partial moment of order $j  1$ for $j$ in $\{1,\dots, n \}$. Closed form expressions for the complete moments are also established. We then focus on $L_p$quantiles, which represent a class of generalized quantiles defined through an asymmetric $p$power loss function. Based on the results obtained, we also show that for a Student $t$ distribution the $L_{nj+1}$quantile and the $L_j$quantile coincide at any confidence level $\tau$ in $(0, 1)$.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.12855
 arXiv:
 arXiv:2209.12855
 Bibcode:
 2022arXiv220912855B
 Keywords:

 Mathematics  Statistics Theory;
 Quantitative Finance  Risk Management
 EPrint:
 18 pages