Access the full text.
Sign up today, get DeepDyve free for 14 days.
R. Yanushkevichius, O. Yanushkevichiene (2002)
New Stability Estimations in P. Lévy's Characterization TheoremJournal of Mathematical Sciences, 111
R. Yanushkevichius, O. Yanushkevichiene (1985)
Stability of P. Lévy's characterization theoremZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 70
J. Kingman, P. Moran (1968)
An introduction to probability theory
W. Feller (1959)
An Introduction to Probability Theory and Its Applications
V. Senatov (1998)
Normal Approximation: New Results, Methods and Problems
Khalid Khan, T. Graham (2018)
Introduction to Probability TheoryIntroduction to Probability Models
In 1923, G. Polya proved that if X 1 and X 2 are independent identically distributed random variables (i.i.d.r.v.) with finite variance, then the distributions of X 1 and (X 1+X 2)/ $$\sqrt 2$$ are coincidental iff X 1 has the normal distribution with zero mean. Is an analogous theorem possible for an couple of statistics X 1 and (X 1+X 2)/21/α if α<2? P. Lévy constructed an example that denies that hypothesis. However, having supplemented the condition of coincidence of the distributions of X 1 and (X 1+X 2)/21/α with a similar condition, namely, requiring, in addition, for the distributions of X 1 and (X 1+X 2+X 3)/31/α to be coincident (here X 1,X 2 and X 3 are i.i.d.r.v.), P. Lévy has proved that X 1 and X 2 have a strictly stable distribution. The stability of this characterization in a metric λ0 (that is defined in the class of characteristic functions by analogy with a uniform metric defined in the class of distributions) without an additional symmetry assumption as well as the stability in a Lévy metric L are analizied in this paper.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 18, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.