• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.583-589
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• 2019

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.265-274
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• 2004

The paper extends earlier work on the skew-normal distribution, a family of distributions including normal, but with extra parameter to regulate skewness. The present work introduces a singly truncated parametric family that strictly includes a truncated normal distribution, and studies its properties, with special emphasis on the relation with bivariate normal distribution.

• 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.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.241-250
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• 2010

Over the past few decades, several studies have been made on the modeling of circular data. But these studies focused mainly on the symmetrical cases including von Mises distribution. Recently, many studies with skew-normal distribution have been conducted in the linear case. In this paper, we dealt the problem of fitting of non-symmetrical circular data with wrapped skew-normal distribution which can be derived by using the principle of wrapping. Wrapped skew-normal distribution is very flexible to asymmetical data as well as to symmetrical data. Multi-modal data are also fitted by using the mixture of wrapped skew-normal distributions. To estimate the parameters of mixture, we suggested the EM algorithm. Finally we verified the accuracy of the suggested algorithm through simulation studies. Application with real data is also considered.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.879-891
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• 2009

We developed the projected l-axial skew-normal(LASN) family of distributions for I-axial data. The LASN family of distributions contains the semicircular skew-normal(SCSN) and the circular skew-normal(CSN) families of distributions as special cases. The LASN densities are similar to the wrapped skew-normal densities for the small values of the scale parameter. However CSN densities have more heavy tails than those of the wrapped skew-normal densities on the circle. Furthermore the CSN densities have two modes as the scale parameter increases. The LASN distribution has very convenient mathematical features. We extend the LASN family of distributions to a bivariate case.

• 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.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.189-199
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• 2020

This paper studies a Bayesian ordered multiple linear regression model with skew normal error. It is reasonable that the kind of inherent information available in an applied regression requires some constraints on the coefficients to be estimated. In addition, the assumption of normality of the errors is sometimes not appropriate in the real data. Therefore, to explain such situations more flexibly, we use the skew-normal distribution given by Sahu et al. (The Canadian Journal of Statistics, 31, 129-150, 2003) for error-terms including normal distribution. For Bayesian methodology, the Markov chain Monte Carlo method is employed to resolve complicated integration problems. Also, under the improper priors, the propriety of the associated posterior density is shown. Our Bayesian proposed model is applied to NZAPB's apple data. For model comparison between the skew normal error model and the normal error model, we use the Bayes factor and deviance information criterion given by Spiegelhalter et al. (Journal of the Royal Statistical Society Series B (Statistical Methodology), 64, 583-639, 2002). We also consider the problem of detecting an influential point concerning skewness using Bayes factors. Finally, concluding remarks are discussed.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1211-1219
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• 2013

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.