• Communications for Statistical Applications and Methods
• /
• v.21 no.4
• /
• pp.285-296
• /
• 2014

The quantile residual life function has been effectively used to interpret results from the analysis of the proportional hazards model for censored survival data; however, the quantile residual life function is not always estimable with currently available semi-parametric regression methods in the presence of heavy censoring. A parametric regression approach may circumvent the difficulty of heavy censoring, but parametric assumptions on a baseline hazard function can cause a potential bias. This article proposes a Bayesian semi-parametric regression approach for inference on an unknown baseline hazard function while adjusting for available covariates. We consider a model-based approach but the proposed method does not suffer from strong parametric assumptions, enjoying a closed-form specification of the parametric regression approach without sacrificing the flexibility of the semi-parametric regression approach. The proposed method is applied to simulated data and heavily censored survival data to estimate various quantile residual lifetimes and adjust for important prognostic factors.

• Journal of the Society of Naval Architects of Korea
• /
• v.44 no.5
• /
• pp.542-550
• /
• 2007

A geometry modification is one of main keys in achieving a successful optimization. The optimized hull form generated from the geometry modification should be a realistic, faired form from the ship manufacturing point of view. This paper presents a practical hull optimization procedure using a parametric modification function. In the parametric modification function method, the initial ship geometry was easily deformed according to the variations of design parameters. For example, bulbous bow can be modified with several parameters such as bulb area, bulb length, bulb height etc. Design parameters are considered as design variables to modify hull form, which can reduce the number of design variables in optimization process and hence reduce its time cost. To verify the use of the parametric modification function, optimization for KCS was performed at its design speed (FN=0.26) and the wave making resistance is calculated using a well proven potential code with fully nonlinear free surface conditions. The design variables used are key design parameters such as Cp curve, section shape and bulb shape. This study shows that the hull form optimized by the parametric modification function brings 7.6% reduction in wave making resistance. In addition, for verification and comparison purpose, a direct geometry variation method using a bell-shape modification function is used. It is shown that the optimal hull form generated by the bell-shaped modification function is very similar to that produced by the parametric modification function. However, the total running time of the parametric optimization is six times shorter than that of the bell shape modification method, showing the effectiveness and practicalness from a designer point of view in ship yards.

• KIPS Transactions on Software and Data Engineering
• /
• v.11 no.1
• /
• pp.1-10
• /
• 2022

Deep neural networks are widely used to solve various problems. In a fully connected neural network, the nonlinear activation function is a function that nonlinearly transforms the input value and outputs it. The nonlinear activation function plays an important role in solving the nonlinear problem, and various nonlinear activation functions have been studied. In this study, we propose a combined parametric activation function that can improve the performance of a fully connected neural network. Combined parametric activation functions can be created by simply adding parametric activation functions. The parametric activation function is a function that can be optimized in the direction of minimizing the loss function by applying a parameter that converts the scale and location of the activation function according to the input data. By combining the parametric activation functions, more diverse nonlinear intervals can be created, and the parameters of the parametric activation functions can be optimized in the direction of minimizing the loss function. The performance of the combined parametric activation function was tested through the MNIST classification problem and the Fashion MNIST classification problem, and as a result, it was confirmed that it has better performance than the existing nonlinear activation function and parametric activation function.

• Journal of the Korean Vacuum Society
• /
• v.12 no.1
• /
• pp.20-24
• /
• 2003

We Performed the modeling of the dielectric functions of InGaAs by using the parametric semiconductor model. Parametric model describes the analytic dielectric function as the summation of several energy-bounded Gaussian-broadened polynomials and provides a reasonably well parameterized function which can accurately reproduce the optical constants of InGaAs materials. We obtained the values of fitting parameters of an arbitrary composition $\chi$ through the parametric model. And then, from these parameters we could obtain the unknown dielectric functions of InGaAs alloy films ($0\leq\chi\leq1$).

• International Journal of Reliability and Applications
• /
• v.1 no.1
• /
• pp.81-87
• /
• 2000

One of the most important quantities in reliability theory is the expected number of renewals of a system during a given interval. This quantity, the renewal function, is used to determine the optimal preventive maintenance policy and to estimate the cost of a warranty. In this paper we study a parametric approach for a renewal function. The simulation study is presented to compare the relative performance of the introduced estimators of a renewal function. And we show that the proposed parametric estimator performs well.

• KIPS Transactions on Software and Data Engineering
• /
• v.10 no.10
• /
• pp.407-420
• /
• 2021

Deep neural networks are widely used to solve various problems. However, the deep neural network with a deep hidden layer frequently has a vanishing gradient or exploding gradient problem, which is a major obstacle to learning the deep neural network. In this paper, we propose a parametric activation function to alleviate the vanishing gradient problem that can be caused by nonlinear activation function. The proposed parametric activation function can be obtained by applying a parameter that can convert the scale and location of the activation function according to the characteristics of the input data, and the loss function can be minimized without limiting the derivative of the activation function through the backpropagation process. Through the XOR problem with 10 hidden layers and the MNIST classification problem with 8 hidden layers, the performance of the original nonlinear and parametric activation functions was compared, and it was confirmed that the proposed parametric activation function has superior performance in alleviating the vanishing gradient.

• KIPS Transactions on Software and Data Engineering
• /
• v.11 no.9
• /
• pp.371-380
• /
• 2022

Convolutional neural networks are widely used to manipulate data arranged in a grid, such as images. A general convolutional neural network consists of a convolutional layers and a fully connected layers, and each layer contains a nonlinear activation functions. This paper proposes a combined parametric activation function to improve the performance of convolutional neural networks. The combined parametric activation function is created by adding the parametric activation functions to which parameters that convert the scale and location of the activation function are applied. Various nonlinear intervals can be created according to parameters that convert multiple scales and locations, and parameters can be learned in the direction of minimizing the loss function calculated by the given input data. As a result of testing the performance of the convolutional neural network using the combined parametric activation function on the MNIST, Fashion MNIST, CIFAR10 and CIFAR100 classification problems, it was confirmed that it had better performance than other activation functions.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1777-1795
• /
• 2015

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.671-697
• /
• 2024

In this paper, we formally introduce the notion of a general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g. trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.

• Journal of Korean Vacuum Science & Technology
• /
• v.6 no.4
• /
• pp.149-152
• /
• 2002

We performed the modeling of the dielectric functions of C $d_{0.77}$M $g_{0.23}$Te by using parametric semiconductor model. Parametric model describes the analytic dielectric function as the summation of several energy-bounded Gaussian-broadened polynomials and provides a reasonably well parameterized function which can accurately reproduce the optical constants of semiconductor materials. We obtained the values of fitting parameters of the Mg composition 0.23 in the parametric model. From these parameters we could remove interference oscillations to obtain the dielectric function of C $d_{0.77}$M $g_{0.23}$Te alloy film for full 0.5-6.0 eV energy range.y range.