**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series A, Pt. 3, pp. 337--341

**A CHARACTERIZATION OF DISCRETE SELF-DECOMPOSABLE DISTRIBUTIONS IN TERMS OF SURVIVAL DISTRIBUTIONS AND THE SELF-DECOMPOSIBILITY OF THE DISCRETE LOGARITHMIC DISTRIBUTION**

By

E. B. FOSAM, *Sheffield Hallam University*

SUMMARY. Shanbag (1977) obtained a characterization of power-series distributions while extending the Rao-Rubin (1964) characterization of the Poisson law. The survival distributions figuring in the Rao-Rubin discussion were characterized by Srivastava and Srivastava (1970), among others. Alzaid (1986) characterized infinitely divisible laws among power series distributions, in terms of survival distributions. The present note is concerned with a similar discussion of self-decomposable discrete laws and an application thereof to prove the self-decomposability of the discrete logarithmic distribution.

*AMS (1980) subject classification.* 60E05, 62E10.

*Key words and phrases.* Discrete self-decomposability, survival distributions, logarithmic distribution.