Study on approximation for cumulative distribution function of doubly non-central F distribution

Ikuo Arizono, Yoma Ishii, Ryosuke Tomohiro, Shingo Inoue, Yasuhiko Takemoto

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Abstract

In recent years, it has been indicated that the statistical feature of the SN ratio, which is famous as a criterion for parameter design using the Taguchi method, is described by a doubly non-central F distribution. Accordingly, the characteristics of the doubly non-central F distribution are gaining attention again. It should be noted that the cumulative distribution function of doubly non-central F distribution is shown based on the incomplete beta function or Gauss hypergeometric function. Since the computations for incomplete beta function and Gauss hypergeometric function are complex, approximations for evaluating the cumulative distribution function of the doubly non-central F distribution have been investigated. In this study, a new approximation for the cumulative distribution function of the doubly non-central F distribution is proposed. Through some numerical validation, the features of the proposed approximation are addressed.

Original languageEnglish
Pages (from-to)257-266
Number of pages10
JournalJournal of Japan Industrial Management Association
Volume66
Issue number3
Publication statusPublished - 2015

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Keywords

  • Approximation by Hastings et al.
  • Approximation by Mudholkar
  • Approximation by Paulson

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Applied Mathematics
  • Management Science and Operations Research
  • Strategy and Management

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