This article is cited in 9 papers

Short Communications

Cauchy equation on discrete domain and some characterisation theorems

R. Dasgupta

Statistics-Mathematics Division, Indian Statistical Institute, Calcutta, India

Abstract: Discrete version of normal distribution, i.e., $P(x)=c\exp\{-\beta x^2\}$, $\beta>0$, $x\in\mathbf{Z}$, is characterised via the solution of cauchy type equation on discrete domain in dimension 4 or higher. It is also shown that this characterisation does not necessarily holds for second and third dimensions. Some statistical aspects of radial symmetry and eccentricity along with the properties of this distribution are also discussed.

Keywords: Cauchy equation, radial symmetry, eccentricity, discrete normal, distribution.

Received: 29.08.1991

Language: English

 English version: Theory of Probability and its Applications, 1993, 38:3, 520–524

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