Study on Approximation for Cumulative Distribution Function of Doubly Non-central <i>F</i> Distribution

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  • 2重非心<i>F</i>分布の累積分布関数の近似に関する研究
  • 2重非心F分布の累積分布関数の近似に関する研究
  • 2ジュウ ヒシン F ブンプ ノ ルイセキ ブンプ カンスウ ノ キンジ ニ カンスル ケンキュウ

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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.

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