• International Journal of CAD/CAM
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• 제13권1호
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• pp.1-11
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• 2013

Just by adjusting the control points iteratively, progressive iterative approximation (PIA) presents an intuitive and straightforward scheme such that the resulting limit curve (surface) can interpolate the original data points. In order to obtain more flexibility, adjusting only a subset of the control points, a new method called local progressive iterative approximation (LPIA) has also been proposed. But to this day, there are two problems about PIA and LPIA: (1) Only an approximation process is discussed, but the accurate convergence curves (surfaces) are not given. (2) In order to obtain an interpolating curve (surface) with high accuracy, recursion computations are needed time after time, which result in a large workload. To overcome these limitations, this paper gives an explicit matrix expression of the control points of the limit curve (surface) by the PIA or LPIA method, and proves that the column vector consisting of the control points of the PIA's limit curve (or surface) can be obtained by multiplying the column vector consisting of the original data points on the left by the inverse matrix of the collocation matrix (or the Kronecker product of the collocation matrices in two direction) of the blending basis at the parametric values chosen by the original data points. Analogously, the control points of the LPIA's limit curve (or surface) can also be calculated by one-step. Furthermore, the $G^1$ joining conditions between two adjacent limit curves obtained from two neighboring data points sets are derived. Finally, a simple LPIA method is given to make the given tangential conditions at the endpoints can be satisfied by the limit curve.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.425-445
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• 2021

A generalization of the log-logistic (LL) distribution called exponentiated log-logistic (ELL) distribution on lines of exponentiated Weibull distribution is considered. In this paper, based on progressive type-II censored samples, we have derived the maximum likelihood estimators and Bayes estimators for three parameters, the survival function and hazard function of the ELL distribution. Then, under the balanced squared error loss (BSEL) and the balanced linex loss (BLEL) functions, their corresponding Bayes estimators are obtained using Lindley's approximation (see Jung and Chung, 2018; Lindley, 1980), Tierney-Kadane approximation (see Tierney and Kadane, 1986) and Markov Chain Monte Carlo methods (see Hastings, 1970; Gelfand and Smith, 1990). Here, to check the convergence of MCMC chains, the Gelman and Rubin diagnostic (see Gelman and Rubin, 1992; Brooks and Gelman, 1997) was used. On the basis of their risks, the performances of their Bayes estimators are compared with maximum likelihood estimators in the simulation studies. In this paper, research supports the conclusion that ELL distribution is an efficient distribution to modeling data in the analysis of survival data. On top of that, Bayes estimators under various loss functions are useful for many estimation problems.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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• pp.1309-1317
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• 2013

일반화 지수분포 (generalized exponential distribution)를 따르는 점진 제 1종 구간 중도절단 (progressive type-I interval censoring) 표본에서 모수 추정은 Chen과 Lio (2010)가 최대우도 추정법 (maximum likelihood estimation), 중간점 근사법 (mid-point approximation method), EM 알고리즘 (expectation maximization algorithm), 적률 추정법 (method of moments estimation; MME)으로 하였으며, 그 방법들 중 평균제곱오차 (mean square error; MSE)가 가장 작은 추정법은 중간점 근사법이다. 하지만 중간점 근사법을 바탕으로 최대우도 추정법을 이용하여 모수를 추정하려고 한다면 모수에 대한 해를 전개할 수 없기 때문에 수치 해석적인 방법을 이용하여 추정하여야 한다. 본 논문에서는 이러한 문제를 해결하기 위해서 근사 최대우도 추정법 (approximate maximum likelihood estimation)을 이용하여 두 종류의 모수를 추정하고, 모의실험을 통하여 수치해석학적인 방법을 이용한 중간점 근사법의 해 (estimate of mid-point approximation method; MP)와 제시한 두 가지 추정량을 평균제곱오차 측면에서 비교한다.

• ETRI Journal
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• 제43권3호
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• pp.447-458
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• 2021

The quality of experience (QoE) of video streaming is degraded by playback interruptions, which can be mitigated by the playout buffers of end users. To analyze the impact of playout buffer dynamics on the QoE of wireless adaptive hypertext transfer protocol (HTTP) progressive video, we model the playout buffer as a G/D/1 queue with an arbitrary packet arrival rate and deterministic service time. Because all video packets within a block must be available in the playout buffer before that block is decoded, playback interruption can occur even when the playout buffer is non-empty. We analyze the queue length evolution of the playout buffer using diffusion approximation. Closed-form expressions for user-perceived video quality are derived in terms of the buffering delay, playback duration, and interruption probability for an infinite buffer size, the packet loss probability and re-buffering probability for a finite buffer size. Simulation results verify our theoretical analysis and reveal that the impact of playout buffer dynamics on QoE is content dependent, which can contribute to the design of QoE-driven wireless adaptive HTTP progressive video management.

• Journal of the Korean Data and Information Science Society
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• 제25권3호
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• pp.643-653
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• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• 대한기계학회논문집A
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• 제24권12호
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• 대한전자공학회논문지SP
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• 제40권1호
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• pp.114-123
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• 2003

본 논문에서는 영상 객체 (object) 의 모양 정보를 효율적으로 부호화 하는 기법을 제안한다. 다각 근사화 기법은 손실 부호화 기법으로써 객체의 모양을 근사화 하는데 가장 널리 사용되고 있다. 제안된 기법은 최대 허용 오차를 만족하면서 정점을 선택할 때 기존의 순환 정점 선택 (IRM: iterated refinement method) 이나 순차적 정점 선택 (PVS: progressive vertex selection) 보다 적은 수의 정점을 선택함으로써 비트량을 줄인다. 기존의 순차적인 정점 선택 기법을 기반으로 하여 새로운 정점 선택 조건을 제안하여 비트량-왜곡면에서 우수한 성능을 가지는 부호화기를 구현하였다. 실험 결과에서 제안된 기법이 기존의 정점 선택 기법들에 비해 우수한 성능을 나타냄을 알 수 있다.

• Journal of the Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• ETRI Journal
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• 제39권1호
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• pp.1-12
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• 2017

In this paper, we present a new approach for the progressive compression of three-dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate-distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub-optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.

• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.