WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
The Modes of Some Distributions in Independent Trials
Authors: , ,
Abstract: By the methods of multivariate transition probability flow graphs, we define the multivariate geometric distribution and the multi-parameter geometric distribution in independent trials, derive their generating functions, probability distributions and the exact modes. For the multinomial distribution, we only get its mode in some cases. It is still an open question for all other cases. Following the multinomial distribution, we state the definition of the multivariate Poisson distribution, and then employ the joint probability generating function of multivariate Poisson distribution to discuss its modes. We also prove that k is the unique mode of the geometric distribution of order k. Finally, we propose some open questions to the interested readers as an objective and challenge for further study.
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Keywords: mode, multivariate geometric distribution, multivariate Poisson distribution, success run, MTPFG, probability generating function
Pages: 280-289
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #27