On discrete distributions of order k (Q5903346)

The class of discrete distributions of order k is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero and from the right away from \(k+1\). The probability function and factorial moments of these distributions are expressed in terms of the (right) truncated Bell (partition) polynomials and several special cases are briefly examined. Finally a Poisson process of order k, leading in particular to the Poisson distribution of order k, is discussed.