English, Article, Journal or magazine article edition: Sums and Extreme Values of Random Variables: Duality Properties Ralph W. Bailey

User activity

Share to:
 
Bookmark: http://trove.nla.gov.au/version/17082
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Sums and Extreme Values of Random Variables: Duality Properties
Author
  • Ralph W. Bailey
Physical Description
  • preprint
Notes
  • The inversion theorem for radially-distributed complex random variables provides a completely symmetric relationship between their characteristic functions and their distribution functions, suitably defi- ?ned. If the characteristic function happens also to be a distribution function, then a dual pair of random variables is de?fined. The distrib- ution function of each is the characteristic function of the other. If we call any distribution possessing a dual partner 'invertible', then both the radial normal and radial t distributions are invertible. Moreover the product of an invertible variable (for instance, a radial normal variable) with any other independent variable is invertible. Though the most prominent examples of invertible variables possess a normal divisor, we exhibit a pair of variables neither of which has a normal di- visor. A test for normal-divisibility, based on complete monotonicity, is provided. The sum of independent invertible variables is invertible; the inverse is the smallest in magnitude of the inverse variables. The- orems about sums of invertible random variables (for instance, central limit theorems) have a dual interpretation as theorems about extrema, and vice versa.
  • Bernstein's theorem; Bessel transform; duality; extreme value theorem; radial distribution; t-distribution
  • RePEc:bir:birmec:09-05
Language
  • English
Contributed by
OAIster

Get this edition

Other links

  • Set up My libraries

    How do I set up "My libraries"?

    In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

  • All (1)
  • Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

User activity


e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition

Be the first to add this to a list

Comments and reviews

What are comments? Add a comment

No user comments or reviews for this version

Add a comment