• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.109-130
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• 2018

Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.809-818
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• 2014

Multivariate skew-normal distribution(distribution that includes multivariate normal distribution) has been recently applied to many application areas. We consider saddlepoint approximation for a statistic of linear combination based on a multivariate skew-normal distribution. This approach can be regarded as an extension of Na and Yu (2013) that dealt saddlepoint approximation for the distribution of a skew-normal sample mean for a linear statistic and multivariate version. Simulations results and examples with real data verify the accuracy and applicability of suggested approximations.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.571-579
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• 2016

Most of studies related to the distributions of quadratic forms are conducted under the assumption of multivariate normal distribution. In this paper, we suggested an approximation to the distribution of quadratic forms based on multivariate skew-normal distribution as alternatives for multivariate normal distribution. Saddlepoint approximations are considered and the accuracy of the approximations are verified through simulation studies.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.373-391
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• 2022

The distribution of observations in most econometric studies with spatial heterogeneity is skewed. Usually, a single transformation of the data is used to approximate normality and to model the transformed data with a normal assumption. This assumption is however not always appropriate due to the fact that panel data often exhibit non-normal characteristics. In this work, the normality assumption is relaxed in spatial mixed models, allowing for spatial heterogeneity. An inference procedure based on Bayesian mixed modeling is carried out with a multivariate skew-elliptical distribution, which includes the skew-t, skew-normal, student-t, and normal distributions as special cases. The methodology is illustrated through a simulation study and according to the empirical literature, we fit our models to non-life insurance consumption observed between 1998 and 2002 across a spatial panel of 103 Italian provinces in order to determine its determinants. Analyzing the posterior distribution of some parameters and comparing various model comparison criteria indicate the proposed model to be superior to conventional ones.

• 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.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.227-244
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• 2023

In this paper, a depth-based nonparametric test for a multivariate two-sample scale problem is proposed. The proposed test statistic is based on the depth-induced ranks and is thus distribution-free. In this article, the depth values of data points of one sample are calculated with respect to the other sample or distribution and vice versa. A comprehensive simulation study is used to examine the performance of the proposed test for symmetric as well as skewed distributions. Comparison of the proposed test with the existing depth-based nonparametric tests is accomplished through empirical powers over different depth functions. The simulation study admits that the proposed test outperforms existing nonparametric depth-based tests for symmetric and skewed distributions. Finally, an actual life data set is used to demonstrate the applicability of the proposed test.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1171-1180
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• 2014

We considered saddlepoint approximations to VaR (value at risk) and ES (expected shortfall) which frequently encountered in finance and insurance as the measures of risk management. In this paper we supposed univariate and multivariate skew-normal distributions, instead of traditional normal class distributions, as underlying distribution of linear portfolios. Simulation results are provided and showed the suggested saddlepoint approximations are very accurate than normal approximations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.8
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• pp.2082-2102
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• 2024

Accurate segmentation of magnetic resonance (MR) images is crucial for providing doctors with effective quantitative information for diagnosis. However, the presence of weak boundaries, intensity inhomogeneity, and noise in the images poses challenges for segmentation models to achieve optimal results. While deep learning models can offer relatively accurate results, the scarcity of labeled medical imaging data increases the risk of overfitting. To tackle this issue, this paper proposes a novel fuzzy c-means (FCM) model that integrates a deep learning approach. To address the limited accuracy of traditional FCM models, which employ Euclidean distance as a distance measure, we introduce a measurement function based on the skewed normal distribution. This function enables us to capture more precise information about the distribution of the image. Additionally, we construct a regularization term based on the Kullback-Leibler (KL) divergence of high-confidence deep learning results. This regularization term helps enhance the final segmentation accuracy of the model. Moreover, we incorporate orthogonal basis functions to estimate the bias field and integrate it into the improved FCM method. This integration allows our method to simultaneously segment the image and estimate the bias field. The experimental results on both simulated and real brain MR images demonstrate the robustness of our method, highlighting its superiority over other advanced segmentation algorithms.