WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
Some Generalizations of Geometric Distribution in Bernoulli Trials by TPFG Methods
Authors: ,
Abstract: In this paper, by the transition probability flow graphs theory, we obtain the transition probability flow graphs of the random variables distributed as Gk(p) and NBk(r; p), the generalizations of usual geometric distribution. We derive their probability generating functions, means, variances and their exact probability distributions, in addition, we reveal the correlation between them. For success runs in n Bernoulli trials, we find the new concise formulae for the probability distributions of Ln and N(k)n . Finally, proceed from the parameter n = 2; 3; 4, we derive the generalized geometric distribution denoted by G(p1, • • • , pn) and discuss its properties base on multivariate transition probability flow graphs methods.
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Keywords: geometric distribution, negative binomial distribution, success run, TPFG methods, probability generating function, probability distribution
Pages: 146-155
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #14