2022/09/26 by Valeria Bignozzi, Bignozzi, Valeria, Luca Merlo +3
Decision Sciences · Engineering · Mathematics · #FOS: Economics and business #FOS: Mathematics #Probabilistic and Robust Engineering Design #Reliability and Maintenance Optimization #Risk Management (q-fin.RM) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2209.12855
openalex publication_date 2022/09/26 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
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 Lp-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 Ln-j+1-quantile and the Lj-quantile coincide at any confidence level τ in (0, 1).