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Complex-valued characteristic functions with (some) real powers — II

✍ Scribed by B. Ramachandran

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
531 KB
Volume
63
Category
Article
ISSN
0378-3758

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✦ Synopsis

It is shown that for every positive integer n ~> 2 and for every p > 0, there exist distributien functions F on the real line ~ such that: (i) F has absolute moments of all orders up to and including p, or up to and not including p, as we choose, and (iit the convolutions F *r of E wilh itself are asymmetric (about the origin) for 1 ~< r ~< n -1, while F *° is asymmetric. This relates to a question raised in Staudte and Tata (Proc.

📜 SIMILAR VOLUMES

Characteristic functions with some power
Characteristic functions with some powers real — III
✍ B. Ramachandran 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 222 KB

It is shown that, for every integer n >t 2, there exist distribution functions F on the real line (which may be chosen to be of lattice type or absolutely continuous) such that (i) F has moments of all orders, and (ii) the convolutions F\*', 1 ~< r ~< n -1, ofF with itself are all asymmetric about t