Componentwise Maxima and Threshold Excess Multivariate Extremes: Mutual Connections, their Simple Extreme Distributions and Random Generation Methods for those Extreme Values

• Kitano Toshikazu

  名古屋工業大学大学院社会工学専攻

Bibliographic Information

Other Title

• 成分毎の最大値と閾値を超過する多変量極値：それらの相互関係，それらの単純極値分布と乱数生成法
• セイブン ゴト ノ サイダイチ ト イキチ オ チョウカ スル タヘンリョウキョクチ : ソレラ ノ ソウゴ カンケイ,ソレラ ノ タンジュンキョクチ ブンプ ト ランスウ セイセイホウ

Abstract

Multivariate extreme value theories are reviewed in the point of view of the intensity of Poisson process of generating the extreme values. Componentwise maxima (CM) have been principally studied in the conventional researches while the multivariate Pareto distribution was derived a quarter century ago to deal with threshold excess multivariate extremes (TEXMEX). It will be found that the essential concepts and perspectives are not yet complete to comprehend the properties of the multivariate extreme value in the practical sense. Thus the mutual connections between CM and TEXMEX are discussed, and it is especially shown not only CM but also TEXMEX employ their own simple distributions to manifest a method of generating their random values simultaneously.

Journal

• Journal of the Japan Statistical Society, Japanese Issue

  Journal of the Japan Statistical Society, Japanese Issue 51 (1), 123-156, 2021-09-15

  Japan Statistical Society

Keywords

• 生起強度
• ポアソン過程
• 包除原理
• 従属関数と相関関数
• 順序統計量
• 停止規則

Details

• CRID: 1390570862077276288
• NII Article ID: 130008088077
• NII Book ID: AA1105098X
• DOI: 10.11329/jjssj.51.123
• ISSN: 21891478
• ISSN: 03895602
• NDL BIB ID: 031781321
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I031781321
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • CiNii Articles
  • KAKEN
  • Crossref
• Abstract License Flag: Disallowed