Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 18--24

A NECESSARY AND SUFFICIENT CONDITION FOR A PROBABILITY DISTRIBUTION FUNCTION TO HAVE AN ENTIRE CHARACTERISTIC FUNCTION OF PERFECTLY REGULAR GROWTH

By

MONIKA DEWESS, University of Leipzig

SUMMARY. Based on results due to L. Davies, B. Ramachandran and M. Riedel, a necessary and sufficient condition is found for a distribution function to have an entire characteristic function of perfectly regular growth with given type. Weibull-distributions and Rayleigh-distributions are examples of such distributions.

AMS (1990) subject classification. 60E10.

Key words and phrases. Entire characteristic function, regular growth.

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