• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.517-527
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• 2005

This paper considers a discrete-time queueing system with variable service capacity. Using the supplementary variable method and the generating function technique, we compute the joint probability distribution of queue length and remaining service time at an arbitrary slot boundary, and also compute the distribution of the queue length at a departure time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• Journal of the Korea Computer Industry Society
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• v.5 no.9
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• pp.921-928
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• 2004

This paper proposed dynamic adaptive model based on discrete probability distribution function and user profile in web based HyperMedia educational systems. This modelsrepresents application domain to weighted direction graph of dynamic adaptive objects andmodeling user actions using dynamically approach method structured on discrete probability function. Proposed probabilitic analysis can use that presenting potential attribute to useractions that are tracing search actions of user in WebMedia structure. This approach methodscan allocate dynamically appropriate profiles to user.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.7
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• pp.1224-1233
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• 1994

The error performance of BPSK and QPSK signals in mobile satellite channel is investigated considering nonlinearity of TWTA (Traveling Wave Tube Amplifier) in the presence of AWGN(Additive White Gaussian Noise) on the uplink and downlink paths. It is assumed that the fading on the downlink path forms a Rician distribution. The Rician distribution is approximated by discrete probability values. The values are firstly found by Classical Moment Technique. Finally, the error probability is evaluated using approximate discrete values of Rician distribution and the Gaussian Quadrature Formula.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.285-295
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• 2001

We consider a queueing system under overload control to support bursty traffic. The queueing system under overload control is modelled by MMBP/D1/K queue with two thresholds on buffer. Arrival of customer is assumed to be a Markov-modulated Bernoulli process (MMBP) by considering burstiness of traffic. Analysis is done in discrete-time case. Using the generating function method, we obtain the stationary queue length distribution. Finally, the loss probability and the waiting time distribution of a customer are given.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1109-1115
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• 2010

In this paper, exact confidence interval of hyper-geometric parameter, that is the probability of success p in the population is discussed. Usually, binomial distribution is a well known discrete distribution with abundant usage. Hypergeometric distribution frequently replaces a binomial distribution when it is desirable to make allowance for the finiteness of the population size. For example, an application of the hypergeometric distribution arises in describing a probability model for the number of children attacked by an infectious disease, when a fixed number of them are exposed to it. Exact confidence interval estimation of hypergeometric parameter is reviewed. We consider the performance of exact confidence interval estimates of hypergeometric parameter in terms of actual coverage probability by small sample Monte Carlo simulation.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.275-282
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• 2010

This paper analyzes a discrete-time bulk-service queue with probabilistic bulk size, where the service process is interrupted by a Markov chain. We study the joint probability generating function of system occupancy and the state of the Markov chain. We derive several performance measures of interest, including average system occupancy and delay distribution.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.119-125
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• 1997

We handle the stochastic processes of independent and identically distributed random variables. But random variables are usually dependent among themselves in actual life. So in this paper, we find out a new process not satisfying Markov property. We investigate the probability mass functions and study on the probability of the first-passage time. Also we find out the average frequency of continuous successes in from 0 to n time.