Computing the Symmetries and Exponents of Operator-Stable Laws

Mark M. Meerschaert
Additional contact information
Mark M. Meerschaert: Albion College, Department of Mathematics

A chapter in Computing Science and Statistics, 1992, pp 461-462 from Springer

Abstract: Abstract If X 1, X 2, X 3, … are i.i.d. random vectors and A n(X 1 + … + X n) - b n converges weakly to a nondegenerate limit Y, then Y is operator-stable. In other words there is a matrix B called an exponent of Y such that for all n = 1,2,3, … if Y1, Y2, Y3, … are i.i.d. with Y then exp(-.B log n)(Y 1 + … + Y n) is identically distributed with Y + a n for some a n. Computation of the norming matrices A n is complicated by the fact that Y may possess a complex symmetry structure. The set of symmetries of Y forms a compact group G with the property that exp(Bs)G exp(-Bs) = G for all real s. We use this fact to compute G. The computer algebra system Maple is used to perform the necessary matrix calculations.

Keywords: Compact Group; Decomposition Theorem; Norming Matrice; National Science Foundation Grant; Jordan Decomposition (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2856-1_76

Ordering information: This item can be ordered from
http://www.springer.com/9781461228561

DOI: 10.1007/978-1-4612-2856-1_76

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().