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Statistical inference for discrete distributions on random sequences

Research Project

Project/Area Number 18540148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKansai University

Principal Investigator

AKI Sigeo  Kansai University, システム理工学部, 教授 (90132696)

Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥2,710,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Keywords離散分布論 / 確率母関数 / 離散パターン / 条件付き期待値 / 最尤推定量 / 複合パターン / スキャン統計量 / 連続システム / 有向木 / 高次マルコフ木 / 2重確率母関数 / マルコフ連鎖 / 最尤推定法 / 確率測度の弱収束 / empirical process / 高次マルコフ連鎖 / start-up demonstration test / 識別可能性
Research Abstract

Exact discrete distributions of numbers of occurrences and waiting times of some patterns and scans on random sequences are investigated. Based on our theoretical new results we can make statistical inference of some parameters such as success probability. By extending the method of conditional probability generating functions we have derived new results analytically, some of which are also suitable for numerical calculations.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (34 results)

All 2009 2008 2007 Other

All Journal Article (26 results) (of which Peer Reviewed: 20 results) Presentation (8 results)

  • [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 Vol.38

      Pages: 621-641

    • Related Report
      2009 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 Vol.61

      Pages: 499-516

    • NAID

      40016615664

    • Related Report
      2009 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] Waiting time distributions for a run with additional constraints2008

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

      Journal of Statistical Planning and Inference 138

      Pages: 3492-3501

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions of waiting time random variables for patterns2008

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

      Journal of the Japan Statistical Society Vol.38,No.1

      Pages: 97-105

    • NAID

      10030993551

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Methods for studying generalized birthday and coupon collection problems2008

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

      Communications in Statistics-Simulation and Computation

      Pages: 844-862

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions of numbers of occurrences in a discrete pattern and weak convergence of an empirical process for the pattern2008

    • Author(s)
      Aki, S
    • Journal Title

      Journal of Multivariate Analysis Vol.99

      Pages: 1460-1473

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions ofnumbers of occurrences of a discretepattern and weak convergence of anempirical process for the pattern2008

    • Author(s)
      Aki S
    • Journal Title

      Journalof Multivariate Analysis 99

      Pages: 1460-1473

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Joint distributions of waiting time randomvariables for patterns,2008

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

      Journal of Japan Statistical Society 38

      Pages: 97-105

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Waiting time distributions for a run with additional constraints2008

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

      Journal of Statistical Planning and Inference 138

      Pages: 3492-3501

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Methods for studying generalized birthday and coupon collection problems2008

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

      Communications in Statistics-Simulation and Computation 37

      Pages: 844-862

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern2008

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

      Journal of Multivariate Analysis 99

      Pages: 1460-1473

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions of waiting time random variables for patterns2008

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

      Journal of the Japan statistical Society 38

      Pages: 97-105

    • NAID

      10030993551

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Waiting time distributions for a run with additional constraints2008

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

      Journal of statistical Planning and Inference 138

      Pages: 3492-3501

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Methods for studying generalized birthday and coupon collection problems2008

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

      Communications in statistics - Simulation and Computation 37

      Pages: 844-862

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions associated with compound patterns in a sequence of Markov dependent multistate trials and estimation problems2007

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

      Journal of the Japan Statistical Society Vol.37

      Pages: 285-298

    • NAID

      110006570585

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent trials2007

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

      Annals of the Institute of Statistical Mathematics Vol.59

      Pages: 577-595

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the waiting time for the success run2007

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

      Annals of the Institute of Statistical Mathematics Vol.59

      Pages: 597-602

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On generating functions of waiting times and numbers of occurrences of compound patterns in a sequence of multistate trials2007

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

      Journal of Applied Probability Vol.44

      Pages: 71-81

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the waiting time for the first success run2007

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

      Annals of the Institute of Statistical Mathematics 59

      Pages: 597-602

    • NAID

      40015577822

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] On the waiting time for the first success run2007

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

      Annals of the Institute of Statistical Mathematics 59

      Pages: 597-602

    • NAID

      40015577822

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent trials2007

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

      Annals of the Institute of Statistical Mathematics 59

      Pages: 577-595

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On generating functions of waiting times and numbers of occurrences ofcomPound Patterns in a sequence of multistate trials2007

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

      Journal of Applied Probabihty 44

      Pages: 71-81

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Joint distributions associated with compound patterns in a sequence ofMarkov dependent multistate trials and estimation problems2007

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

      Journal of the Japan Statistical Society 37

      Pages: 285-298

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Waiting time distributions for a run with additional constraints

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

      Journal of Statistical Planning and Inference (印刷中)

    • Related Report
      2006 Annual 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(京田辺市)
    • Year and Date
      2009-09-09
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] 離散パターンの数に関するempirical processについて2009

    • Author(s)
      安芸重雄
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2009-03-27
    • Related Report
      2009 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2009年度年会
    • Place of Presentation
      東京大学(東京都)
    • Year and Date
      2009-03-27
    • Related Report
      2009 Final Research Report
  • [Presentation] 離散パターンの数に関するempirical processについて2009

    • Author(s)
      安芸重雄
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-27
    • Related Report
      2008 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
      日本数学会年会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] On generalized birthday and coupon collection problems2008

    • Author(s)
      井上潔司, 安芸重雄
    • Organizer
      2008年度統計関連学会連合大会
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2008-09-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] パターンの待ち時間の同時分布について2007

    • Author(s)
      安芸 重雄、平野 勝臣
    • Organizer
      2007年度統計関連学会連合大会
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-09-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] パターンの待ち時間分布と識別可能性問題2007

    • Author(s)
      井上 潔司、安芸 重雄
    • Organizer
      2007年度統計関連学会連合大会
    • Place of Presentation
      神戸大学
    • Year and Date
      2007-09-08
    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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