Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 10--17

ON THE LOWER TYPE OF AN ENTIRE CHARACTERISTIC FUNCTION OF A PROBABILITY DISTRIBUTION

By

MONIKA DEWESS, University of Leipzig

SUMMARY. A theorem of Jakoleva (1976) on the lower order of an entire characteristic function of a probability distribution is the starting point to find a similar result on the type. From an asymptotical tail condition on an interval sequence, the lower type of an entire characteristic function is derived. Examples of distribution functions are presented satisfying the required tail conditions. Their characteristic functions are entire, having both a given type and a given lower type.

AMS (1980) subject classification. 60E10.

Key words and phrases. Tails of distributions.

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