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Statistical distribution theory on graphs

Research Project

Project/Area Number 24540141
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionSeikei University

Principal Investigator

INOUE Kiyoshi  成蹊大学, 経済学部, 教授 (10384653)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords離散分布論 / 数え上げ問題 / アルゴリズム / 離散分布理論 / 信頼性工学 / 統計的分布理論 / 統計的推測理論 / グラフ
Outline of Final Research Achievements

I considered the three topics:「Discrete distribution theory on undirected graphs」,「Distribution theory of discrete patterns on directed acyclic graphs」,「On dual relationships between discrete distributions on bivariate sequences」. I proposed the methods and algorithm for deriving the probability distribution exactly. The illustrative examples are also given in order to demonstrate the feasibility of the methods and algorithm. Furthermore, I presented these results at five conferences and I published five papers on the above topics.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (10 results)

All 2015 2014 2013 2012

All Journal Article (6 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results) Presentation (4 results)

  • [Journal Article] Distributions of numbers of runs and scans on higher order Markov directed acyclic graphs with generation2015

    • Author(s)
      Inoue, K.
    • Journal Title

      Josai Mathematical Monographs

      Volume: 8 Pages: 3-16

    • NAID

      120005575962

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 確率・統計に登場する超幾何2014

    • Author(s)
      井上潔司、竹村彰通
    • Journal Title

      数学セミナー2014年3月号

      Volume: 53 Pages: 19-23

    • Related Report
      2013 Research-status Report
  • [Journal Article] On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials2013

    • Author(s)
      Inoue, K. and Aki, S.
    • Journal Title

      Metrika

      Volume: Online First Issue: 7 Pages: 895-920

    • DOI

      10.1007/s00184-013-0478-0

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs2013

    • Author(s)
      Kiyoshi Inoue, Aki, S. and Balakrishnan Narayanaswamy
    • Journal Title

      Methodology and Computing in Applied Probability

      Volume: 15 Issue: 2 Pages: 349-362

    • DOI

      10.1007/s11009-011-9246-7

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Distributions of numbers of runs and scans on directed acyclic graphs with generation2013

    • Author(s)
      Inoue, K. and Aki, S.
    • Journal Title

      Computational Statistics

      Volume: 28 Issue: 3 Pages: 1133-1150

    • DOI

      10.1007/s00180-012-0349-6

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Exact distributions of the number of pattern occurrences in undirected graphical models2012

    • Author(s)
      Aki, S. and Inoue, K.
    • Journal Title

      Journal of the Japan Statistical Society

      Volume: Vol. 42 Pages: 59-79

    • NAID

      10030867431

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Distributions of numbers of runs and scans on higher order Markov directed acyclic graphs with generation2014

    • Author(s)
      井上 潔司
    • Organizer
      ワークショップ「統計科学とその周辺」
    • Place of Presentation
      城西大学
    • Year and Date
      2014-12-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非サイクル有向グラフ上の連, スキャンの分布2014

    • Author(s)
      井上潔司、安芸重雄
    • Organizer
      2014年度日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 向きのないグラフィカルモデル上の離散パターンの数の分布2013

    • Author(s)
      安芸重雄,井上潔司
    • Organizer
      2013年度日本数学会年会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Distributions of simple patterns in some kinds of exchangeable sequences2012

    • Author(s)
      井上潔司,安芸重雄
    • Organizer
      2012年 統計関連学会 連合大会
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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