• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.337-347
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• 2024

Kernel density estimation is a prevalent technique employed for nonparametric density estimation, enabling direct estimation from the data itself. This estimation involves two crucial elements: selection of the kernel function and the determination of the appropriate bandwidth. The selection of the bandwidth plays an important role in kernel density estimation, which has been developed over the past decade. A range of methods is available for selecting the bandwidth, including the plug-in bandwidth. In this article, the proposed plug-in bandwidth is introduced, which leverages shifted Chebyshev series-based approximation to determine the optimal bandwidth. Through a simulation study, the performance of the suggested bandwidth is analyzed to reveal its favorable performance across a wide range of distributions and sample sizes compared to alternative bandwidths. The proposed bandwidth is also applied for kernel density estimation on real dataset. The outcomes obtained from the proposed bandwidth indicate a favorable selection. Hence, this article serves as motivation to explore additional plug-in bandwidths that rely on function approximations utilizing alternative series expansions.

• Journal of Advanced Navigation Technology
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• v.17 no.4
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• pp.429-434
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• 2013

In this paper, the TM (Transverse Magnetic) scattering problems by a perfectly conducting strip grating over a grounded two dielectric layers with edge boundary condition are analyzed by applying the FGMM (Fourier Galerkin Moment Method). For the TM scattering problem, the induced surface current density is expected to the very high value at both edges of the strip, then the induced surface current density on the conductive strip is expanded in a series of the multiplication of the Chebyshev polynomials of the first kind and the functions of appropriate edge boundary condition. Generally, when the value of the relative permittivity of dielectric layers over the ground plane increased, the strip width according to the sharp variation points of the reflected power is shifted to a higher value. The numerical results shown the fast convergent solution and good agreement compared to those of the existing papers.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.171-182
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• 2018

For the first time, nonlocal damped vibration and buckling analyses of arbitrary tapered bidirectional functionally graded solid circular nano-plate (BDFGSCNP) are presented by employing modified spectral Ritz method. The energy method based on Love-Kirchhoff plate theory assumptions is applied to derive neutral equilibrium equation. The Eringen's nonlocal continuum theory is taken into account to capture small-scale effects. The characteristic equations and corresponding first mode shapes are calculated by using a novel modified basis in spectral Ritz method. The modified basis is in terms of orthogonal shifted Chebyshev polynomials of the first kind to avoid employing adhesive functions in the spectral Ritz method. The fast convergence and compatibility with various conditions are advantages of the modified spectral Ritz method. A more accurate multivariable function is used to model two-directional variations of elasticity modulus and mass density. The effects of nanoscale, in-plane pre-load, distributed dashpot, arbitrary tapering, pinned and clamped boundary conditions on natural frequencies and buckling loads are investigated. Observing an excellent agreement between results of current work and outcomes of previously published works in literature, indicates the results' accuracy in current work.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.7
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• pp.694-704
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• 2011

In this paper, we present a design of a 5th order Chebyshev interdigital band-pass filter using inverter and susceptance slope parameter values obtained from EM simulated multi-port Y-parameters. The shifted length of the resonator is determined when the frequency of the transmission zero is separated far away from the center frequency. For the initial dimensions of the interdigital filter, the filter is decomposed into the individual resonators, and the dimensions are obtained using EM Simulation of the decomposed resonators. However, the interdigital filter with the dimensions determined from the EM simulation of the decomposed resonators shows slightly distorted response from the desired frequency response due to the coupling between non-adjacent resonators. To obtain a EM simulation dataset, EM simulation for this filter is carried out by parameter sweep with constant ratio for the initial values. In this dataset, it is determined the final values for the filter by optimization. The fabricated filter by PCB shows an upper-shift of center frequency of about 70 MHz, which was caused by permittivity changed and tolerance of fabrication.