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How are moments and moments of spacings related to distribution functions?

Jones, M. C. and Balakrishnan, N. (2002). How are moments and moments of spacings related to distribution functions? Journal of Statistical Planning and Inference, 103(1-2) pp. 377–390.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/S0378-3758(01)00232-4
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Abstract

It is shown how rth moments of random variables and rth product moments of spacings between random variables can be written as r-dimensional integrals involving only the distribution function, and not the density or any other function of the variables of integration. These fundamental formulae are the main focus of the paper and appear to be new for r≥3, as well as for the second cross-moment of spacings. The formulae for ordinary moments are derived separately for r=3 and 4. Those for moments of spacings allow an expression for quite general r. Links with L-moments and with expressions for the moments of the sample range are explored. Extensions to the independent but not identically distributed case are given.

Item Type: Journal Article
Copyright Holders: 2002 Elsevier Science B.V.
ISSN: 0378-3758
Keywords: kurtosis; L-moments; non-identically distributed random variables; order statistics; range; skewness
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22670
Depositing User: Sarah Frain
Date Deposited: 11 Aug 2010 11:29
Last Modified: 02 Dec 2010 21:02
URI: http://oro.open.ac.uk/id/eprint/22670
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