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Let X(1),⋯,X(k),X(k+1) be random variables that take nonnegative integer values and let (∗) ∑(i,1,k+1)X(i)=n. The joint distribution of the first k variables is given by the probability function p(x(1),⋯,x(k))=P(X(1)=x(1),⋯,X(k)=x(k)). A truncation of the component X(i) of the vector X=(X(1),⋯,X(k)) is defined by the constraint b(i)≤X(i)≤n, where b(i) is a positive integer. The author obtains an expression...
The authors continue the study of incomplete moments of discrete distributions by Gerstenkorn [Rev. Roumaine Math. Pures Appl. 26 (1981), no. 3, 405–416; MR0627288; Bull. Inst. Internat. Statist. 46 (1975), no. 3, 290–297; MR0471020]. For a discrete nonnegative random variable X, the left incomplete factorial moment of order l truncated at s is defined by ∑sx=0x(x−1)⋯(x−(l−1))P(X=x). The authors evaluate...
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