Arismendi Zambrano, Juan (2013) Multivariate truncated moments. Journal of Multivariate Analysis, 117. pp. 41-75. ISSN 0047-259X

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Abstract

We derive formulae for the higher order tail moments of the lower truncated multivariate standard normal (MVSN), Student’s , lognormal and a finite-mixture of multivariate normal distributions (FMVN). For the MVSN we propose a recursive formula for moments of arbitrary order as a generalization of previous research. For the Student’s -distribution, the recursive formula is an extension of the normal case and when the degrees of freedom V→∞ the tail moments converge to the normal case. For the lognormal, we propose a general result for distributions in the positive domain. Potential applications include robust statistics, reliability theory, survival analysis and extreme value theory. As an application of our results we calculate the exceedance skewness and kurtosis and we propose a new definition of multivariate skewness and kurtosis using tensors with the moments in their components. The tensor skewness and kurtosis captures more information about the shape of distributions than previous definitions.

Item Type:	Article
Keywords:	Truncated moments; Extreme moments; Censored data;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	10209
Identification Number:	https://doi.org/10.1016/j.jmva.2013.01.007
Depositing User:	Juan Arismendi Zambrano
Date Deposited:	12 Nov 2018 15:22
Journal or Publication Title:	Journal of Multivariate Analysis
Publisher:	Elsevier
Refereed:	Yes
URI:	https://www.sciencedirect.com
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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