• Corpus ID: 252531495

Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles

@inproceedings{Bignozzi2022InterorderRB,
  title={Inter-order relations between moments of a Student \$t\$ distribution, with an application to \$L\_p\$-quantiles},
  author={Valeria Bignozzi and Luca Merlo and Lea Petrella},
  year={2022}
}

• V. Bignozzi, Luca Merlo, L. Petrella
• Published 26 September 2022
• Mathematics

This paper introduces inter-order 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 , . . . , 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 n − j +1 -quantile and the L j -quantile coincide at any confidence level τ in (0 , 1).