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Urn designs with immigration: Useful connection with continuous time stochastic processes
Affiliation:1. Columbia, MO, USA;2. Baltimore, MD, USA;1. Department of Public Health, University of Aberdeen, Aberdeen, UK;2. Health Services Research Unit, University of Aberdeen, Aberdeen, UK;1. Institute of Statistical Science, Academia Sinica, 128, Sec. 2 Academia Road, Taipei 11529, Taiwan;2. Department of Statistics, Columbia University, New York, NY 10027, USA;1. Department of Statistic and Operations Research, Faculty of Pharmacy, Campus de Cartuja, University of Granada, 18071 Granada, Spain;2. Department of Statistic and Operations Research, Faculty of Sciences, University of Granada, 18071 Granada, Spain;1. Departamento de Estadı́stica e Investigación Operativa, Universidad Pública de Navarra, Campus de Arrosadı́a s/n, Pamplona 31006, Spain;2. Departamento de Métodos Estadı́sticos, Universidad de Zaragoza, Facultad de Ciencias, Pedro Cerbuna, 12, Zaragoza 50009, Spain;1. Department of Statistics and Applied Probability, National University of Singapore, 3 Science Drive 2, Singapore, 117543, Singapore;2. Department of Statistics, University of Wisconsin, Madison, USA;3. Department of Statistics, Northeast Normal University, Jilin 130024, PR China
Abstract:In this paper we present techniques that allow obtaining joint and marginal distributions of random variables arising in urn designs with immigration. The urn is embedded into a family of continuous time Markov processes. Then the generating function approach is used to obtain distributional results. A randomized version of the inverse sampling is introduced.
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