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: https://doi.org/10.1016/S0378-3758(01)00232-4

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 22670
• Item Type
• Journal Item
• ISSN
• 0378-3758
• Keywords
• kurtosis; L-moments; non-identically distributed random variables; order statistics; range; skewness
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2002 Elsevier Science B.V.
• Depositing User
• Sarah Frain