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Characteristic functions with some powers real — III

✍ Scribed by B. Ramachandran

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
222 KB
Volume
34
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 the origin, while F*" is symmetric. This answers a question raised in Staudte and Tata (1970) and rounds off earlier work of the present author. Incidentally, new families of distribution functions with moments of all orders and with all members of the same family having the same moment sequence are obtained. (Earlier examples of such families are due to Lebesgue and Heyde.

📜 SIMILAR VOLUMES

Complex-valued characteristic functions
Complex-valued characteristic functions with (some) real powers — II
✍ B. Ramachandran 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 531 KB

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