论文标题
学生的瞬间$ t $分布之间的订购关系，并申请$ l_p $ - Quantiles
Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles
论文作者
论文摘要
本文介绍了$ n $ n $自由度的学生的$ t $分布的部分和完整时刻的间订单公式。我们展示了如何根据$ j $ j -1 $ in $ \ {1，\ dots，n \} $表示任何实际值$ m $的部分订单$ n -j $。还建立了整个时刻的封闭表达式。然后，我们专注于$ L_P $ - Quantiles，该Quantiles代表通过非对称$ p $ -power损耗功能定义的一类广义分位数。根据获得的结果，我们还表明，对于学生$ t $分布，$ l_ {n-j+1} $ - Quantile和$ l_j $ - Quantile-Quantile Comincide in Duspuse级别$τ$ in $（0，1）$。
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 $\{1,\dots, n \}$. 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 $L_{n-j+1}$-quantile and the $L_j$-quantile coincide at any confidence level $τ$ in $(0, 1)$.
