• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.513-523
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• 2016

Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.901-909
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• 2013

A skewed double power function distribution is defined by a double power function distribution. We shall evaluate the coefficient of the skewness of a skewed double power function distribution. We shall obtain an approximate maximum likelihood estimator (MLE) and a moment estimator (MME) of the skew parameter in the skewed double power function distribution, and compare simulated mean squared errors for those estimators. And we shall compare simulated MSEs of two proposed reliability estimators in two independent skewed double power function distributions with different skew parameters.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.58-62
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• 1990

Air gap flux density is obtained strictly from air gap permeance and MMF distribution using the design parameter of BLDCM when the stator slot is considered. Then the theoretical equations representing the cogging torque and BEMF are proposed. The effect of skew is described analytically, and skew effect on air gap permeance and MMF is studied. Consequently we verified analytically that skew of slots and magnets influenced on the reduction of the cogging torque and BEMF ripple, and the shape of BEMF.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.5
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• pp.26-35
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• 2003

Propellers operating in a given nonuniform ship wake generate unsteady loads leading to undesirable stern vibration problems. The skew is known to be the most proper and effective geometric parameter to control or reduce the fluctuating forces on the shaft. This paper assumes the skew profile as either a quadratic or a cubic function of the radius and determines the coefficients of the polynomial function by applying the simplex method. The method uses the converted unconstrained algorithm to solve the constrained minimization problem of 6-component shaft excitation forces. The propeller excitation was computed either by applying the two-dimensional gust theory for quick estimation or by the fully three-dimensional unsteady lifting surface theory in time domain for an accurate solution. A sample result demonstrates that the shaft forces can be further reduced through optimization from the original design.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1105-1109
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• 2009

This paper deals with a polynomial thrust equation of a permanent magnet linear synchronous motor that is considered by a skew and overhang effects of permanent magnet. The skew length, the overhang length, the width and height of permanent magnet, the teeth length and air-gap length which effect to the flux density of air-gap are selected as variables of the polynomial thrust equation. Polynomial thrust equation is elicited by the 6 parameters. The results are satisfied that the values by polynomial thrust equation are compared ones by using 3-dimensional finite element analysis and experiment.

• Journal of the Korean Data and Information Science Society
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• v.20 no.4
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• pp.733-740
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• 2009

We obtain a skewed uniform distribution by a uniform distribution, and evaluate its coeffcient of skewness. And we obtain the approximate maximum likelihood estimator (AML) and moment estimator of skew parameter in the skewed uniform distribution. And we compare simulated mean squared errors (MSE) of those estimators, and also compare MSE of two proposed reliability estimators in two independent skewed uniform distributions each with different skew parameters.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.6
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• pp.607-613
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• 2009

In this paper, we made a simple paper feeding system which is one of MTS (media transport system) and controllers. The plant has a flexible paper and two driving rollers and two driven rollers. The control system has two conventional PID controllers. Skew angle and feeding speed of MTS deteriorate the quality of feeding system. In order to control a feeding speed and skew of feeding paper, we control rotational velocity of two driving rollers. Therefore, this controller has two inputs and two outputs as MIMO (multi-input and multi-output) system. The control inputs were the feeding speed and the skew displacement of the paper. The control outputs were the rotational velocity to each driving roller. To find appropriate PID gains of two controllers, we proposed an optimization technique. We assume the system variables and performance of a whole system as follows. PID gains of two controllers for skew and feeding speed are system variables. System performance is both skew and feeding speed. We simulates to making mathematical correlation using global Kriging interpolation. To find appropriate value of system variables, optimization method is simulation in sequence as following method. First, the optimization solver simulates with DOE (design of experiment) tables to find correlation equation of both system variable and performances. Then, the solver guesses the appropriate values and simulates if the system variables are appropriate or not. If the result of validation doesn't satisfy the convergence and iteration tolerance, the solver makes a new Kriging models and iterates this sequence until satisfy the tolerances.

• Communications for Statistical Applications and Methods
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• v.23 no.4
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• pp.321-334
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• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.

• Steel and Composite Structures
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• v.28 no.4
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• pp.509-516
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• 2018

The differential quadrature (DQ) and teaching-learning based optimization (TLBO) methods are coupled to introduce a hybrid numerical method for maximizing fundamental natural frequency of laminated composite skew plates. The fiber(s) orientations are selected as design variable(s). The first-order shear deformation theory (FSDT) is used to obtain the governing equations of the plate. The equations of motion and the related boundary conditions are discretized in space domain by employing the DQ method. The discretized equations are transferred from the time domain into the frequency domain to obtain the fundamental natural frequency. Then, the DQ solution is coupled with the TLBO method to find the maximum frequency of the plate and its related optimum stacking sequences of the laminate. Convergence and applicability of the proposed method are shown and the optimum fundamental frequency parameter of the plates with different skew angle, boundary conditions, number of layers and aspect ratio are obtained. The obtained results can be used as a benchmark for further studies.