TY - JOUR
T1 - Random-allocation and urn models
AU - Gani, J.
PY - 2004
Y1 - 2004
N2 - We review some urn and random-allocation models, mostly using probability generating function (PGF) methods. We begin by formulating a basic problem which can be thought of as either an urn or a random-allocation model; a PGF solution to it is outlined. When the compartments in the latter model are no longer homogeneous, the multivariate PGF can still be derived, though the algebra becomes cumbersome. Some results are given for the case where there are two types of compartment and for the case where there are two types of ball. Some comments are offered on the Frobenius-Harper property of PGFs.
AB - We review some urn and random-allocation models, mostly using probability generating function (PGF) methods. We begin by formulating a basic problem which can be thought of as either an urn or a random-allocation model; a PGF solution to it is outlined. When the compartments in the latter model are no longer homogeneous, the multivariate PGF can still be derived, though the algebra becomes cumbersome. Some results are given for the case where there are two types of compartment and for the case where there are two types of ball. Some comments are offered on the Frobenius-Harper property of PGFs.
KW - Nonhomogeneous balls
KW - Nonhomogeneous compartments
KW - PGF methods
KW - Random-allocation models
KW - Urn models
UR - http://www.scopus.com/inward/record.url?scp=33845726078&partnerID=8YFLogxK
U2 - 10.1239/jap/1082999068
DO - 10.1239/jap/1082999068
M3 - Review article
SN - 0021-9002
VL - 41 A
SP - 313
EP - 320
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - SPEC. ISSUE
ER -