Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 1--7

COMPLEX VALUED CHARACTERISTIC FUNCTIONS WITH (SOME) REAL POWERS

By

B. RAMACHANDRAN, Indian Statistical Institute

SUMMARY.  It is shown that, for every positive integer $n \geq 2$, there exist distribution functions F on the Real line such that (i) the convolutions F*r are asymmetric for $1 \leq r \lt n$, while F*n is symmetric; and (ii) F has absolute moments of all orders < 11 -providing a partial answer to a question raised by Staudte and Tata. (In two sequels, it is shown that (ii) it can be replaced, respectively, by : (ii') F has absolute moments upto and including / not including any order p 0; (ii'') F has moments of all orders.)

AMS (1990) subject classification.  Primary 60E10; secondary 60E05.

Key words and phrases. Characteristic function, symmetric asymmetric distributions, moments, infinite divisibility.

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