caa a22 4500 477062695 CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00049297 doi (NATIONALLICENCE)springer-10.1007/BF00049297 Moment solution to an urn model [Elektronische Daten] [L. Shenton, K. Bowman] A subset of Bernard's RD-model (replenishment-depletion) is considered from the viewpoint of the calculus of finite differences. The most general case is considered and includes an urn with balls of many colors, each color being replenished either deterministically or stochastically. Factorial moment generating functions (fmgfs) are employed to define probability generating functions. A new result is given for the two color case defining the fmgf and probability generating function (with probabilities) when the replenishments are positive valued random variables with given factorial moments. This result involves beta integral transforms defining a manifold of discrete distributions. Particular cases relate to hypergeometric discrete distributions. The Institute of Statistical Mathematics, 1996 Bernard's urn nationallicence beta integral transforms nationallicence finite difference calculus nationallicence generating function nationallicence hypergeometric distributions nationallicence hypergeometric functions nationallicence moments nationallicence replenishment-depletion urn nationallicence Shenton L. Department of Statistics, University of Georgia, 30602, Athens, GA, U.S.A. aut Bowman K. Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, 37831-6367, Oak Ridge, TN, U.S.A. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 169-184 0020-3157 48:1<169 1996 48 10463 https://doi.org/10.1007/BF00049297 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049297 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shenton L. Department of Statistics, University of Georgia, 30602, Athens, GA, U.S.A aut NATIONALLICENCE 700 1- Bowman K. Computer Science and Mathematics Division, Oak Ridge National Laboratory, P.O. Box 2008, 37831-6367, Oak Ridge, TN, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 169-184 0020-3157 48:1<169 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer