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