Discrete multivariate truncated distributions

T. Gerstenkorn. "Discrete multivariate truncated distributions." Mathematica Applicanda 6.12 (1978): null. <http://eudml.org/doc/292755>.

@article{T1978,
abstract = {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},
author = {T. Gerstenkorn},
journal = {Mathematica Applicanda},
keywords = {Exact distribution theory},
language = {eng},
number = {12},
pages = {null},
title = {Discrete multivariate truncated distributions},
url = {http://eudml.org/doc/292755},
volume = {6},
year = {1978},
}

TY - JOUR
AU - T. Gerstenkorn
TI - Discrete multivariate truncated distributions
JO - Mathematica Applicanda
PY - 1978
VL - 6
IS - 12
SP - null
AB - 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
LA - eng
KW - Exact distribution theory
UR - http://eudml.org/doc/292755
ER -