Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Modeling sharply peaked asymmetric multi-modal circular data using wrapped Laplace mixture

겹친라플라스 혼합분포를 통한 첨 다봉형 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 : 2010.06.27
  • Accepted : 2010.08.28
  • Published : 2010.09.30
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Abstract

Until now, many studies related circular data are carried out, but the focuses are mainly on mildly peaked symmetric or asymmetric cases. In this paper we studied a modeling process for sharply peaked asymmetric circular data. By using wrapped Laplace, which was firstly introduced by Jammalamadaka and Kozbowski (2003), and its mixture distributions, we considered the model fitting problem of multi-modal circular data as well as unimodal one. In particular we suggested EM algorithm to find ML estimates of the mixture of wrapped Laplace distributions. Simulation results showed that the suggested EM algorithm is very accurate and useful.

지금까지 원형자료의 적합에 대한 연구는 주로 von Mises, 겹친왜정규 분포를 비롯하여 주로 완만한 봉우리를 가지는 대칭 및 비대칭의 경우에 대해 수행되어 왔다. 본 논문에서는 뾰족한 봉우리를 가지며 정점을 중심으로 비대칭의 경향이 심한 첨봉형의 비대칭 원형자료에 대한 적합을 다루었다. 최근 Jammalamadaka와 Kozubowski (2003)가 소개한 겹친라플라스 분포와 그의 혼합분포를 중심으로 단봉형 및 다봉형의 원형자료에 대한 모형화 과정을 다루었다. 특히 혼합분포의 모수추정을 위해 EM 알고리즘을 사용하였으며, 모의실험을 통해 그 정확도를 확인하였다.

Keywords

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