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Discrete distribution theory with its statistical applications

Research Project

Project/Area Number 21740083
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionSeikei University

Principal Investigator

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

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords統計数学 / アルゴリズム / 確率モデル / 連 / 確率分布 / 離散分布 / 円周モデル / 母関数 / 信頼性工学 / 推定問題 / パターン / グラフ / マルコフ性 / 双対性
Research Abstract

I considered the three topics :「Discrete distribution theory on graphs」,「Distribution theory of discrete patterns in exchangeable sequences」,「On dual relationships between discrete distributions」. 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 six papers on the above topics.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (26 results)

All 2011 2010 2009 Other

All Journal Article (15 results) (of which Peer Reviewed: 11 results) Presentation (10 results) Remarks (1 results)

  • [Journal Article] Generating functions of waiting times and numbers of visits for random walks on graphs2011

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

      Methodology and Computing in Applied Probability

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bivariate Fibonacci polynomials of order k with statistical applications2011

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

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.63 Pages: 197-210

    • NAID

      40017654623

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of simple patterns in some kinds of exchangeable sequence2011

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

      Journal of Statistical Planning and Inference

      Volume: Vol.141 Pages: 2532-2544

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of simple patterns in some kinds of exchangeable sequences2011

    • Author(s)
      Kiyoshi Inoue, Sigeo Aki, Katuomi Hirano
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 141 Issue: 8 Pages: 2532-2544

    • DOI

      10.1016/j.jspi.2011.02.002

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bivariate Fibonacci polynomials of order k with statistical applications2011

    • Author(s)
      Kiyoshi Inoue, Sigeo Aki
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 63 Issue: 1 Pages: 197-210

    • DOI

      10.1007/s10463-008-0217-x

    • NAID

      40017654623

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the conditional and unconditional distributions of the number of success runs on a circle with applications2010

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

      Statistics and Probability Letters

      Volume: Vol.80 Pages: 874-885

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the conditional and unconditional distributions of the number of success runs on a circle with applications2010

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

      Statistics and Probability Letters

      Volume: 80 Pages: 874-885

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scans on a directed trees2010

    • Author(s)
      井上潔司, 安芸重雄
    • Journal Title

      日本数学会 統計数学分科会 講演アブストラクト

      Pages: 155-156

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 連,スキャン,パターンの分布理論とその応用2010

    • Author(s)
      井上潔司
    • Journal Title

      日本数学会 統計数学分科会 講演アブストラクト

      Pages: 101-120

    • Related Report
      2010 Annual Research Report
  • [Journal Article] On waiting time distributions associated with compound patterns in a sequence of multi-state trials2009

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

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.61 Pages: 499-516

    • NAID

      40016615664

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of runs and scans on higher order Markov trees2009

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

      Communications in Statistics-Theory and Methods

      Volume: Vol.38(5) Pages: 621-641

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On waiting time distributions associated with compound patterns in a sequence of multi-state trials2009

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

      Annals of the Institute of Statistical Mathematics 61

      Pages: 499-516

    • NAID

      40016615664

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distributions of runs and scans on higher order Markov trees2009

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

      Communications in Statistics - Theory and Methods 38

      Pages: 621-641

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 一般化された誕生日問題2009

    • Author(s)
      井上潔司、安芸重雄
    • Journal Title

      日本数学会統計数学分科会講演アブストラクト

      Pages: 85-86

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 有向木上の連の分布2009

    • Author(s)
      井上潔司、安芸重雄
    • Journal Title

      統計関連学会連合大会講演報告集

      Pages: 300-300

    • Related Report
      2009 Annual Research Report
  • [Presentation] Scans on a directed trees2011

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学会 統計数学分科会
    • Place of Presentation
      慶応大学
    • Year and Date
      2011-03-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] 可換試行列上の連の分布2011

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学2011年度春季総合分科会統計数学分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2011 Final Research Report
  • [Presentation] 可換試行列上の連の分布2011

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学会2011年度春季総合分科会統計数学分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] 連,スキャン,パターンの分布理論とその応用2010

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学会2010年度秋季総合分科会統計数学分科会特別講演
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] 連,スキャン,パターンの分布理論とその応用2010

    • Author(s)
      井上潔司
    • Organizer
      日本数学会 統計数学分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Scans on a directed trees2010

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学会2010年度春季総合分科会統計数学分科会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 有向木上の連の分布2009

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      2009年度統計関連学会連合大会
    • Place of Presentation
      同志社大学
    • Year and Date
      2009-09-09
    • Related Report
      2011 Final Research Report
  • [Presentation] 有向木上の連の分布2009

    • Author(s)
      井上潔司、安芸重雄
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      同志社大学
    • Year and Date
      2009-09-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] 一般化された誕生日問題2009

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      日本数学会2009年度春季総合分科会統計数学分科会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2011 Final Research Report
  • [Presentation] 一般化された誕生日問題2009

    • Author(s)
      井上潔司、安芸重雄
    • Organizer
      日本数学会統計数学分科会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-27
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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