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For a sequence X = { X  1 , ... ,  X   n  , ... } of independent identically distributed random variables, we construct the  s -tuples  Y i  ( s ) = ( X i  , ... ,  X  i + s -1  ),  i  = 1, 2, ... ,  n , and consider the random variables  F   i   =  f ( Y i  ( s )),  i  = 1, 2, ... , where  f  is a function defined on the set  R  s  and taking non-negative integer values.

discrete mathematics and applications

The compound Poisson distribution of the number of matches of values of a discrete function of  s -tuples in segments of a sequence of random variables