Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Modeling on asymmetric circular data using wrapped skew-normal mixture

겹친왜정규혼합분포를 이용한 비대칭 원형자료의 모형화

  • Na, Jong-Hwa (Department of Information and Statistics, Chungbuk National University) ;
  • Jang, Young-Mi (Korea Health and Welfare Information Service)
  • 나종화 (충북대학교 정보통계학과) ;
  • 장영미 (한국보건복지정보개발원)
  • Received : 2010.01.14
  • Accepted : 2010.03.19
  • Published : 2010.03.31
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Abstract

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.

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.

Keywords

References

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