• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.153-161
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• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.25-35
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• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1115-1132
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• 1999

We consider a supercritical multitype age dependent branching process. We define a stochastic process Zf(t) which is a functional of the empirical age distribution. When the limit of the expectation of this functional vanishes we4 find some sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.809-816
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• 2011

A tree-indexed autoregressive(AR) process is a time series defined on a tree which is generated by a branching process and/or a deterministic splitting mechanism. This short article is concerned with conditional heteroscedastic structure of the tree-indexed AR models. It has been usual in the literature to analyze conditional mean structure (rather than conditional variance) of tree-indexed AR models. This article pursues to identify quadratic conditional heteroscedasticity inherent in various tree-indexed AR models in a unified way, and thus providing some perspectives to the future works in this area. The identical conditional variance of sisters sharing the same mother will be referred to as the branching heteroscedasticity(BH, for short). A quasilikelihood but preliminary estimation of the quadratic BH is discussed and relevant limit distributions are derived.

• Journal of the Korean Data and Information Science Society
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• v.25 no.5
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• pp.1137-1149
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• 2014

Since the bifurcating autoregressive (BAR) model was developed by Cowan and Staudte (1986) to analyze cell lineage data, a lot of research has been directed to BAR and its generalizations. Based mainly on the author's works, this paper is concerned with a contemporary review on the BAR in terms of an overview and perspectives. Specifically, bifurcating structure is extended to multi-cast tree and to branching tree structure. The AR(1) time series model of Cowan and Staudte (1986) is generalized to tree structured random processes. Branching correlations between individuals sharing the same parent are introduced and discussed. Various methods for estimating parameters and related asymptotics are also reviewed. Consequently, the paper aims to give a contemporary overview on the BAR model, providing some perspectives to the future works in this area.

• The Mathematical Education
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• v.27 no.1
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• pp.55-60
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• 1988

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• The Journal of the Korea Contents Association
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• v.11 no.8
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• pp.475-487
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• 2011

In this paper, we present a systematic method to derive spectrum of high-order pulse and a novel design of e-Learning system that deals with deriving the spectrum using concept-based branching method. Spectrum of high-order pulse can be derived using conventional methods including 'Consecutive Differentiations' or 'Convolutions', however, their complexity of calculation should be too high to be used as the order of the pulse increase. We develop a recursive algorithm according to the order of pulse, and then derive the formula of spectrum connected to the order with a newly designed look-up table. Moving along, we design an e-Learning content for studying the procedure of deriving high-order pulse spectrum described above. In this authoring, we use the concept-based object branching method including conventional page or title-type branching in sequential playing. We design all four Content-pages divided into 'Modeling', 'Impulse Response and Transfer Function', 'Parameters' and 'Look-up Table' by these conceptual objects. And modules and sub-modules are constructed hierarchically as conceptual elements from the Content-pages. Students can easily approach to the core concepts of the analysis because of the effects of our new teaching method. We offer step-by-step processes of the e-Learning content through unit-based branching scheme for difficult modules and sub-modules in our system. In addition we can offer repetitive learning processes for necessary block of given learning objects. Moreover, this method of constructing content will be considered as an advanced effectiveness of content itself.

• Journal of English Language & Literature
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• v.56 no.6
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• pp.1191-1210
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• 2010

This article claims that English liquid consonants are characterized by the presence of complex place nodes, regardless of dialectal varieties. The primary difference between rhotic and laterals can be pursued in a phonological sense. The level of subbranching nodes is in charge of the disparities among two types of liquids: the branching immediately below the Coronal node with laterals, while branching at the secondary sublevel with rhotics. In this context, the processes of rhotic deletion and lateral vocalization can be understood as those motivated to get rid of complex place nodes. That is, those processes take place as part of phonological attrition. Next, the onset/coda asymmetry regarding liquids stems from the dispreference of vocoid at the onset position, which is readily accounted for by the series of constraints on the well-formedness on the onset, namely Harmonic Onset. The rationale of gradualness and harmonic improvement proposed by Harmonic Serialism is useful to separate the attested outputs from unattested ones across the whole gamut of English varieties. All in all, the primary benefits of our analysis can be found in the consistence in the explanation for the operations running through the sounds regarded as belonging to liquid consonants, comprising the whole range of rhotic and lateral consonants.