• Communications for Statistical Applications and Methods
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• 제26권6호
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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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• 제11권2호
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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.

• 응용통계연구
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• 제27권5호
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• pp.809-818
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• 2014

다변량 왜정규분포는 다변량 정규분포를 포함하는 분포로 최근 많은 응용분야에서 활용되고 있다. 본 논문에서는 다변량 왜정규분포를 기반으로 하는 선형결합통계량의 분포함수에 대한 안장점근사를 다루었다. 이는 단변량 왜정규분포 기반 표본평균에 대한 Na와 Yu (2013)의 결과를 선형결합 및 다변량의 경우로 확장한 것이다. 모의실험과 실제자료분석을 통해 제안된 근사법의 유용성과 정확도를 확인하였다.

• Communications for Statistical Applications and Methods
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• 제25권2호
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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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• 제21권2호
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• pp.241-250
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• 2010

원형자료에 대한 모형화 분석은 주로 von Mises 분포를 비롯한 대칭형의 경우를 중심으로 많은 연구가 이루어져 왔다. 최근 선형자료의 분석에서 다양한 비대칭의 자료에 적합한 왜정규분포의 활용에 대한 연구가 활발히 수행되고 있다. 본 논문에서는 Pewsey (2000a)에 의해 처음 소개된 겹친왜정규분포를 이용한 비대칭의 원형자료에 대한 적합을 다루었다. 특히 비대칭 다봉형 원형자료의 적합을 위해 겹친왜정규혼합분포를 제안하고, EM 알고리즘을 통한 모수추정 과정을 제시하였다. 모의실험을 통해 EM 알고리즘을 통한 모수추정의 정확성을 확인하고, 실제 지방국도의 일일교통량 자료의 모형화 분석에 적용하였다.

• 응용통계연구
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• 제22권4호
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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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• 제29권3호
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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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• 제27권2호
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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.

• 응용통계연구
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• 제29권4호
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• pp.571-579
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• 2016

이차형식 통계량의 분포함수에 대한 연구는 주로 다변량 정규분포의 가정하에서 진행되어 왔다. 최근 다변량 정규분포를 포함하는 다변량 왜정규분포에 대한 연구가 활발하다. 본 논문에서는 다변량 왜정규분포의 가정하에서 이차형식 통계량의 분포함수에 대한 근사를 다루었다. 근사의 방법으로는 소표본에서도 정확도가 뛰어난 근사법으로 알려진 안장점근사를 사용하였으며, 모의실험을 통해 그 정도를 확인하였다.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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• pp.1211-1219
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• 2013

최근 많은 통계 이론과 응용 문제에 정규분포의 대안으로 왜정규분포에 대한 활용이 높아지고 있다. 본 논문에서는 왜정규분포에 기반한 표본평균의 분포함수에 대한 안장점근사를 다루었다. 안장점근사는 기존의 정규근사에 비해 매우 뛰어난 정확성을 보일 뿐 아니라, 소표본에서도 정확한 근사결과를 제공한다. 본 논문에서 제시한 왜정규분포에 관련된 안장점근사는 복잡한 계산이 요구되는 기존의 Gupta와 Chen (2001)과 Chen 등 (2004)에 대한 근사적 방법으로 사용될 수 있다. 모의실험을 통해 표본평균의 분포함수에 대한 제안된 안장점근사의 정확도를 확인하고, 실제 자료에 대한 응용으로 Roberts (1966)의 쌍둥이 자료의 분석에 적용하였다.