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Statistical Inference for Discrete Patterns

Research Project

Project/Area Number 11640116
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 InstitutionOsaka University

Principal Investigator

AKI Sigeo  Osaka University, Graduate School of Engineering Science, Associate Professor, 大学院・基礎工学研究科, 助教授 (90132696)

Co-Investigator(Kenkyū-buntansha) TANIGUCHI Masanobu  Osaka University Graduate School of Engineering Science, Associate Professor, 大学院・基礎工学研究科, 助教授 (00116625)
INAGAKI Nobuo  Osaka University Graduate School of Engineering Science, Professor, 大学院・基礎工学研究科, 教授 (10000184)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsdiscrete patterns / discrete distribution theory / directed tree / probability generating function / Markov chain / system reliability / binomial distribution / waiting time problems / 離散分布 / パターン / 連 / 工学的システム / 信頼性 / 経験分布関数
Research Abstract

We have studied waiting time distributions of runs and patterns in random structures such as sequences of random variables and random directed trees. The following results are derived.
1. We have obtained the exact distribution of the number of "1" -runs of a specified length on {0, 1} -valued Markov trees. This result can be applied to calculate the reliability of a consecutive system on a directed tree. We also obtained the exact distribution of the life time of the consecutive system on the directed tree.
2. We have studied exact distributions of sooner and later waiting times for runs in Markov dependent bivariate trials. We have given systems of linear equations with respect to conditional probability generating functions of the waiting times and have solved them. This result can be applied to calculate the reliability of the linear connected- (r, s) -out-of- (r+1, n) : F lattice system.
3. We have introduced a Markov chain imbeddable vector of multinomial type and a Markov chain imbeddable variables of returnable type and have discussed some of their properties. By using the result we have derived the distribution of numbers of occurrences of runs of specified lengths in a sequence of multi-state trials.
4. We have introduced a unified counting scheme for runs called 1-overlapping counting. We have given exact probability generating function of the number of 1-overlapping 1-runs of a specified length in some dependent random sequences such as a Markov chain and a heigher order Markov chain.
5. We have introduced a new type of dependent sequence called a binary sequence of order (k, r) and have derived the exact distributions of sooner and later waiting times for success and failure runs in the sequence.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Han,Q.and Aki,S.: "Joint distributions of runs of multi-state trials"Annals of the Institute of Statistical Mathematics. 51. 419-447 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hallin,M.,Taniguchi,M., et al.: "Local asymptotic normality for regression models with long memory disturbance"Annals of Statistics. 27. 2054-2080 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kumagai,E.and Inagaki,N.: "The circular mechanism in the curved exponential family"Methematica Japonica. 49. 27-38 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Aki,S.and Hirano,K.: "Numbers of success-runs of specified length until certain stopping time rules and generalized binomial distributions of order k"Annals of the Institute of Statistical Mathematics. 52. 767-777 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han,Q.and Aki,S.: "Sooner and later waiting time problems based on a dependent sequence"Annals of the Institute of Statistical Mathematics. 52. 407-414 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han,Q.and Aki,S.: "Waiting time problems in a two-state Markov chain"Annals of the Institute of Statistical Mathematics. 52. 778-789 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han, Q.and Aki, S.: "Joint distributions of runs in a sequence of multi-state trials"Ann.Inst.Statist.Math.. 51, No.3. 419-447 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hallin, M., Taniguchi, M., Serroukh, A.and Choy, K.: "Local asymptotic normality for regression models with long memory disturbance"Ann.Statist.. 27, No.6. 2054-2080 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kumagai, E.and Inagaki, N.: "The circular mechanism in the curved exponential family"Mathematica Japonica. 49. 27-38 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Aki, S.and Hirano, K.: "Numbers of success-runs of specified length until certain stopping time rules and generalized binomial distributions of order κ"Ann.Inst.Statist.Math.. 52, No.4. 767-777 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han, Q.and Aki, S.: "Sooner and later waiting time problems based on a dependent sequence"Ann.Inst.Statist.Math.. 52, No.3. 407-414 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han, Q.and Aki, S.: "Waiting time problems in a two-state Markov chain"Ann.Inst.Statist.Math.. 52, No.4. 778-789 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han, S.and Aki, S.: "A unified approach to binomial- type distributions of order κ"Commun.Statist.-Theory Math.. 29(8). 1929-1943 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Han,Q.and Aki,S.: "Joint distributions of runs of multi-state trials"Annals of the Institute of Statistical Mathematics. 51. 419-447 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Hallin,M.,Taniguchi,M., et al.: "Local asymptotic normality for regression models with long memory disturbance"Annals of Statistics. 27. 2054-2080 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kumagai,E.and Inagaki,N.: "The circular mechanism in the curved exponential family"Mathematica Japonica. 49. 27-38 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Aki,S.and Hirano,K.: "Numbers of success-runs of specified length until certain stopping time rules and generalized binomial distributions of order k"Annals of the Institute of Statistical Mathematics. 52. 767-777 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Han,Q.and Aki,S.: "Sooner and later waiting time problems based on a dependent sequence"Annals of the Institute of Statistical Mathematics. 52. 407-414 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Han,Q.and Aki,S.: "Waiting time problems in a two-state Markov chain"Annals of the Institute of Statistical Mathematics. 52. 778-789 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Aki S.: "Distributions of runs and consecutive systems ondirected trees"Annals of the Institute of Statistical Mathematics. 51・1. 1-5 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Aki S.and Hirano K.: "Sooner and later waiting time problems for runs in Markov dependent bivariate trials"Annals of the Institute of Statistical Mathematics. 51・1. 17-29 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Han Q.and Aki S.: "Joint distributions of runs in a sequence of multi-state trials"Annals of the Institute of Statistical Mathematics. 51・3. 419-447 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Aki S.and Hirano K.: "Numbers of success runs of specified length until certain stopping rules and generalized bionominal distributions of order k"Annals of the Institute of Statistical Mathematics. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Han Q.and Aki S.: "Sooner and later waiting time problems based on a dependent sequence"Annals of the Institute of Statistical Mathematics. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Han Q.and Aki S.: "Waiting time problems in a two-state Markov chain"Annals of the Institute of Statistical Mathematics. (発表予定).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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