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2012 Fiscal Year Final Research Report

A circular stochastic process with asymmetric errors

Research Project

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Project/Area Number 22740076
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

KATO Shogo  統計数理研究所, 大学共同利用機関等の部局等, 助教 (60468535)

Project Period (FY) 2010 – 2012
Keywords統計数学 / 円周上のデータ / 非対称分布
Research Abstract

Time series of circular data arise in a number of scientific fields. For example, a series of wind directions measured hourly at a weather station can be considered an example of time series of circular data. Another example is a time series of directions of movements of migratory birds observed in biology. In our study we have proposed a circular autoregressive process with asymmetric angular errors and investigated some properties of the proposed process. An application of the proposed model has been briefly discussed.

  • Research Products

    (26 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (5 results) (of which Peer Reviewed: 3 results) Presentation (20 results) Remarks (1 results)

  • [Journal Article] An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion2013

    • Author(s)
      Kato, S. and Jones, M.C.
    • Journal Title

      Bernoulli

      Volume: 19 Pages: 154-171

    • DOI

      doi:10.3150/11-BEJ397.

    • Peer Reviewed
  • [Journal Article] 円周上のコーシー分布と関連した統計モデル2012

    • Author(s)
      加藤昇吾
    • Journal Title

      日本数学会 2012年度 秋季総合分科会 講演アブストラクト

      Pages: 105-121

  • [Journal Article] Robust estimation of location and concentration parameters for the von Mises-Fisher distribution2012

    • Author(s)
      Kato, S. and Eguchi, S.
    • Journal Title

      arXiv

      Volume: 1201 Pages: 1-37

    • URL

      http://arxiv.org/abs/1201.6476.

  • [Journal Article] Projective power entropy and maximum Tsallis entropy distributions2011

    • Author(s)
      Eguchi, S., Komori, O. and Kato, S.
    • Journal Title

      Entropy

      Volume: 13 Pages: 1746-1764

    • DOI

      doi:10.3390/e13101746.

    • Peer Reviewed
  • [Journal Article] A Markov process for circular data2010

    • Author(s)
      Kato, S.
    • Journal Title

      Journal of the Royal Statistical Society, Series B (Statistical Methodology)

      Volume: 72 Pages: 655-672

    • DOI

      doi:10.1111/j.1467-9868.2010.00748.x.

    • Peer Reviewed
  • [Presentation] Trigonometric momentによって特徴づけられる円周上の確率分布2012

    • Author(s)
      加藤昇吾
    • Organizer
      統計数理セミナー
    • Place of Presentation
      統計数理研究所, 立川
    • Year and Date
      2012-10-10
  • [Presentation] 円周上のコーシー分布と関連した統計モデル2012

    • Author(s)
      加藤昇吾
    • Organizer
      日本数学会 2012年度 秋季総合分科会
    • Place of Presentation
      九州大学, 福岡
    • Year and Date
      2012-09-20
  • [Presentation] A family of distributions on the circle with links to, and an application arising from, Mobius transformation2012

    • Author(s)
      加藤昇吾, Jones, M.C.
    • Organizer
      2012年度 統計関連学会連合大会
    • Place of Presentation
      北海道大学, 札幌
    • Year and Date
      2012-09-11
  • [Presentation] Regression analysis of circular data. Workshop on Directional Statistics2012

    • Author(s)
      Kato, S.,
    • Organizer
      Satellite Office of the Institute of Statistical Mathematics
    • Place of Presentation
      Tokyo,Japan
    • Year and Date
      2012-07-05
  • [Presentation] Robust estimation of location and concentration parameters for the von Mises-Fisher distribution2012

    • Author(s)
      Kato, S. and Eguchi, S.
    • Organizer
      The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      Tsukuba University, Tsukuba,Japan
    • Year and Date
      2012-07-04
  • [Presentation] A family of circular distributions arising from Brownian motion2012

    • Author(s)
      Kato, S.
    • Organizer
      Keio-Yonsei Workshop
    • Place of Presentation
      Yokohama,Japan
    • Year and Date
      2012-05-24
  • [Presentation] A Mobius transformation induced distribution on the torus2012

    • Author(s)
      Kato, S.
    • Organizer
      ISM-ISI-ISSAS Joint Conference 2012
    • Place of Presentation
      The Institute of Statistical Mathematics, Tokyo,Japan
    • Year and Date
      2012-02-03
  • [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion2011

    • Author(s)
      Kato, S., Jones, M.C.
    • Organizer
      International Conference on Advances in Probability and Statistics - Theory and Applications: A Celebration of N. Balakrishnan's 30 Years of Contributions to Statistics
    • Place of Presentation
      Chinese University of Hong Kong, Hong Kong, China
    • Year and Date
      2011-12-29
  • [Presentation] An extended family of circular distributions related to wrapped Cauchy distributions2011

    • Author(s)
      加藤昇吾, Jones, M.C.
    • Organizer
      2011年度 統計関連学会連合大会
    • Place of Presentation
      九州大学, 福岡
    • Year and Date
      2011-09-07
  • [Presentation] An extension of the wrapped Cauchy distribution via Brownian motion. Complex Phenomena from Statistical Point of View2011

    • Author(s)
      Kato, S.
    • Organizer
      Seismology, Environmentology and Economy
    • Place of Presentation
      Meiji University, Kawasaki, Japan
    • Year and Date
      2011-09-01
  • [Presentation] 2変量角度データのための確率分布と関連した統計モデル2011

    • Author(s)
      加藤昇吾
    • Organizer
      統計数理セミナー
    • Place of Presentation
      統計数理研究所, 立川
    • Year and Date
      2011-06-29
  • [Presentation] A Markov process for circular data. Seminar on Mathematical Sciences Based on Modeling2011

    • Author(s)
      Kato, S.
    • Organizer
      Analysis and Simulation
    • Place of Presentation
      Meiji University, Kawasaki, Japan
    • Year and Date
      2011-02-24
  • [Presentation] A distribution for a pair of unit vectors generated by Brownian motion2011

    • Author(s)
      加藤昇吾
    • Organizer
      今野・梶原研究室セミナ
    • Place of Presentation
      横浜国立大学, 横浜
    • Year and Date
      2011-02-08
  • [Presentation] A family of distributions on the circle with links to Mobius transformation2010

    • Author(s)
      加藤昇吾, Jones, M.C.
    • Organizer
      日本数学会 2010年度 秋季総合分科会
    • Place of Presentation
      名古屋大学, 名古屋
    • Year and Date
      2010-09-24
  • [Presentation] 角度データの回帰分析2010

    • Author(s)
      加藤昇吾
    • Organizer
      統計数理研究所 共同利用研究集会「生物群集の多様性と統計数理」
    • Place of Presentation
      統計数理研究所, 立川
    • Year and Date
      2010-09-14
  • [Presentation] 円周上に値をとるマルコフ過程2010

    • Author(s)
      加藤昇吾
    • Organizer
      統計数理セミナー
    • Place of Presentation
      統計数理研究所, 立川
    • Year and Date
      2010-05-19
  • [Presentation] A Markov process for circular data2010

    • Author(s)
      加藤昇吾
    • Organizer
      統計数学セミナー
    • Place of Presentation
      東京大学, 東京
    • Year and Date
      2010-04-28
  • [Presentation] A family of distributions on the circle with links to, and applications arising from, Mobius transformation2010

    • Author(s)
      Kato, S.
    • Organizer
      Two-Day Conference on Statistics and Probability
    • Place of Presentation
      Indian Statistical Institute,Kolkata, India
    • Year and Date
      2010-01-22
  • [Presentation] A family of distributions on the circle with links to, and applications arising from2009

    • Author(s)
      加藤昇吾, Jones, M.C.
    • Organizer
      Mobius transformation. 科研費研究集会「非対称分布の統計学」
    • Place of Presentation
      慶應義塾大学, 横浜
    • Year and Date
      2009-11-25
  • [Presentation] A Markov process for circular time series2009

    • Author(s)
      Kato, S.
    • Organizer
      Workshop "Directional, Asymptotic, Differential-Geometric Statistics and Related Area"
    • Place of Presentation
      Osaka Prefecture University, Sakai,Japan
    • Year and Date
      2009-11-06
  • [Remarks]

    • URL

      http://www.ism.ac.jp/souran/kenkyusya/kato_shogo.html

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Published: 2014-08-29  

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