• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.279-288
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• 1999

In many cases where the conventional binomial distribution fails to apply to real world data, it is mainly due to the lack of independence among Bernoulli trials. Several authors have proposed models that are useful when independence assumption is not satisfied. In this paper, one proposed model is adapted, and estimators of dependence related parameter that is crucial in defining that model are considered. Simulation is performed to compare two estimators(method of moment estimator and maximum likelihood estimator) of dependence related parameter, and conclusions are made.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.3
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• pp.204-215
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• 1988

This paper deals with the adaptive state estimation which is designed specially for a tracking system containing unknown and/or radomly varying hybride noises to provide an accurate estimate of the system state. The range of discrete vectyor v in finite numbers(N) for this adaptive estimator span the entire possible range of impulse noise levels such as the binomial, the edge, the Tchebyscheff, the binomal-edge and the Tchbyscheff-edge distribution. A feed forward path consisting of zero detector and data selector is incoporated with the conventional adaptive state estimator so as to provide accurate estimations. Despite the large and randomly varying hybrid noises, results of computer simulations for the various discrete vector levels show that this adptive state estimator is turned out to be a good system with relatively small implse errors.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.143-152
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• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.6A
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• pp.652-658
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• 2008

In this paper, a new random access scheme is proposed to improve the probability of successful access. In the conventional scheme, a packet is transmitted by a user using one slot and considered successfully transmitted if a collision does not occur. In comparison, a packet of the proposed scheme is transmitted by a user using one or more slots and considered successfully transmitted if there is at least one slot without collision. We evaluate the optimal number of slots selected by users to maximize the probability of successful access when the probability distribution functions for the number of users are given such as Binomial and Poission distribution. From the numerical analysis, it is shown that the proposed scheme performs better than conventional scheme.