Discrete multivariate truncated distributions

T. Gerstenkorn

Mathematica Applicanda, Tome 6 (1978) no. 12, pp. 77-90.

Résumé

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 for the probability function p∗(x(1),⋯,x(t),x(t+1),⋯,x(k)) of the vector X∗, which is obtained by truncating the first t components of the vector X (in view of (∗), the set of possible values of the remaining components also narrows). As an application he considers an urn scheme that reduces to a multivariate (in particular, truncated) Pólya distribution. This work supplements the author's previous paper

Détail

DOI : 10.14708/ma.v6i12.1322

Classification : 62E15
Mots-clés : Exact distribution theory