ACTA issues

On the distribution of sums of overlapping products

Tamás F. Móri

Acta Sci. Math. (Szeged) 67:3-4(2001), 833-841

Abstract. We consider a series of overlapping products of the form $X_1X_2+X_2X_3+X_3X_4+\cdots $ where $X_1,X_2,\ldots $ are independent Bernoulli random variables. We compute the exact distribution of every tail section for a particular choice of the $X$'s, thus extending a result of Csörgő and Wu [2]. As a generalization, sums of multiple products are also studied.

AMS Subject Classification (1991): 60E05, 62E15

Keyword(s): Ewens sampling formula, beta mixture of Poisson distribution, generating function

Received March 1, 2001, and in revised form May 24, 2001. (Registered under 2821/2009.)