Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 4, Pages 291-305

Problem of uniqueness in the renewal process generated by the uniform distribution

D. Ugrin-Šparac

ETF, University of Zagreb, Department of Mathematics, Unska 3, P.P. 148, Zagreb 41001, Croatia

Received 1 February 1992; Revised 1 October 1992

Copyright © 1992 D. Ugrin-Šparac. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The renewal process generated by the uniform distribution, when interpreted as a transformation of the uniform distribution into a discrete distribution, gives rise to the question of uniqueness of the inverse image. The paper deals with a particular problem from the described domain, that arose in the construction of a complex stochastic test intended to evaluate pseudo-random number generators. The connection of the treated problem with the question of a unique integral representation of Gamma-function is also mentioned.