Statistical inference for discrete distributions on random sequences

• Project/Area Number: 18540148
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kansai 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: ¥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.

Research Products

• [Journal Article] Distributions of runs and scans on higher-order Markov trees (2009)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Communications in Statistics-Theory and Methods Vol.38 Pages: 621-641
  • Peer Reviewed
• [Journal Article] On waiting time distributions associated with compound patterns in a sequence of multi-state trials (2009)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Annals of the Institute of Statistical Mathematics Vol.61 Pages: 499-516
  • NAID: 40016615664
  • Peer Reviewed
• [Journal Article] On waiting time distributions associated with compound patterns in a sequence of multi-state trials (2009)
  • Author(s): Inoue, K., Aki, S.
  • Journal Title: Annals of the Institute of Statistical Mathematics 61 Pages: 499-516
  • NAID: 40016615664
  • Peer Reviewed
• [Journal Article] Distributions of runs and scans on higher-order Markov trees (2009)
  • Author(s): Inoue, K., Aki, S.
  • Journal Title: Communications in Statistics-Theory and Methods 38 Pages: 621-641
  • Peer Reviewed
• [Journal Article] Waiting time distributions for a run with additional constraints (2008)
  • Author(s): Aki, S., Hirano, K
  • Journal Title: Journal of Statistical Planning and Inference 138 Pages: 3492-3501
  • Peer Reviewed
• [Journal Article] Joint distributions of waiting time random variables for patterns (2008)
  • Author(s): Aki, S., Hirano, K
  • Journal Title: Journal of the Japan Statistical Society Vol.38,No.1 Pages: 97-105
  • NAID: 10030993551
  • Peer Reviewed
• [Journal Article] Methods for studying generalized birthday and coupon collection problems (2008)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Communications in Statistics-Simulation and Computation Pages: 844-862
  • Peer Reviewed
• [Journal Article] Joint distributions of numbers of occurrences in a discrete pattern and weak convergence of an empirical process for the pattern (2008)
  • Author(s): Aki, S
  • Journal Title: Journal of Multivariate Analysis Vol.99 Pages: 1460-1473
  • Peer Reviewed
• [Journal Article] Joint distributions ofnumbers of occurrences of a discretepattern and weak convergence of anempirical process for the pattern (2008)
  • Author(s): Aki S
  • Journal Title: Journalof Multivariate Analysis 99 Pages: 1460-1473
• [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
• [Journal Article] Waiting time distributions for a run with additional constraints (2008)
  • Author(s): Aki S. and Hirano K
  • Journal Title: Journal of Statistical Planning and Inference 138 Pages: 3492-3501
• [Journal Article] Methods for studying generalized birthday and coupon collection problems (2008)
  • Author(s): Inoue K. and Aki S
  • Journal Title: Communications in Statistics-Simulation and Computation 37 Pages: 844-862
• [Journal Article] Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern (2008)
  • Author(s): Aki, S.
  • Journal Title: Journal of Multivariate Analysis 99 Pages: 1460-1473
  • Peer Reviewed
• [Journal Article] Joint distributions of waiting time random variables for patterns (2008)
  • Author(s): Aki, S., Hirano, K.
  • Journal Title: Journal of the Japan statistical Society 38 Pages: 97-105
  • NAID: 10030993551
  • Peer Reviewed
• [Journal Article] Waiting time distributions for a run with additional constraints (2008)
  • Author(s): Aki, S., Hirano, K.
  • Journal Title: Journal of statistical Planning and Inference 138 Pages: 3492-3501
  • Peer Reviewed
• [Journal Article] Methods for studying generalized birthday and coupon collection problems (2008)
  • Author(s): Inoue, K., Aki, S.
  • Journal Title: Communications in statistics - Simulation and Computation 37 Pages: 844-862
  • Peer Reviewed
• [Journal Article] Joint distributions associated with compound patterns in a sequence of Markov dependent multistate trials and estimation problems (2007)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Journal of the Japan Statistical Society Vol.37 Pages: 285-298
  • NAID: 110006570585
  • Peer Reviewed
• [Journal Article] Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent trials (2007)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Annals of the Institute of Statistical Mathematics Vol.59 Pages: 577-595
  • Peer Reviewed
• [Journal Article] On the waiting time for the success run (2007)
  • Author(s): Aki, S., Hirano, K
  • Journal Title: Annals of the Institute of Statistical Mathematics Vol.59 Pages: 597-602
  • Peer Reviewed
• [Journal Article] On generating functions of waiting times and numbers of occurrences of compound patterns in a sequence of multistate trials (2007)
  • Author(s): Inoue, K., Aki, S
  • Journal Title: Journal of Applied Probability Vol.44 Pages: 71-81
  • Peer Reviewed
• [Journal Article] On the waiting time for the first success run (2007)
  • Author(s): Aki S. and Hirano K
  • Journal Title: Annals of the Institute of Statistical Mathematics 59 Pages: 597-602
  • NAID: 40015577822
• [Journal Article] On the waiting time for the first success run (2007)
  • Author(s): Aki, S.and Hirano, K.
  • Journal Title: Annals of the Institute of Statistical Mathematics 59 Pages: 597-602
  • NAID: 40015577822
  • Peer Reviewed
• [Journal Article] Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent trials (2007)
  • Author(s): Inoue, K.and Aki, S.
  • Journal Title: Annals of the Institute of Statistical Mathematics 59 Pages: 577-595
  • Peer Reviewed
• [Journal Article] On generating functions of waiting times and numbers of occurrences ofcomPound Patterns in a sequence of multistate trials (2007)
  • Author(s): Inoue, K.and Aki, S.
  • Journal Title: Journal of Applied Probabihty 44 Pages: 71-81
  • Peer Reviewed
• [Journal Article] Joint distributions associated with compound patterns in a sequence ofMarkov dependent multistate trials and estimation problems (2007)
  • Author(s): Ihoue, K.and Aki, S.
  • Journal Title: Journal of the Japan Statistical Society 37 Pages: 285-298
  • 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)
• [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
• [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
• [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
• [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
• [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
• [Presentation] On generalized birthday and coupon collection problems (2008)
  • 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
• [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
• [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