日本統計学会誌

ON BALANCED ARRAYS OF 2 SYMBOLS, STRENGTH 2l, m CONSTRAINTS AND INDEX SET {μ₀, μ₁, …, μ_2l} WITH μ_l=0

Teruhiro Shirakura

1975 年 5 巻 2 号 p. 53-56
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.53

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Consider a balanced array (“partially balanced” array, in the terminology of Chakravarti [1]) of 2 symbols, strength 2l, m constraints and index set {μ₀, μ₁, …, μ_2l}. Then it is shown that balanced arrays with μ_l=0 are simple. A necessary and sufficient condition for the existence of such balanced arrays is given.

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NECESSARY AND SUFFICIENT CONDITION FOR THE REDUCIBILITY OF ASSOCIATION SCHEMES

Kumaichi Kusumoto

1975 年 5 巻 2 号 p. 57-64
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.57

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A necessary and sufficient condition for an m-class association scheme to be reducible is given in terms of the characteristic matrix of the association scheme. A method of constructing a new series of association schemes which are called two level m-factorial association schemes is also shown.

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SOME MODIFIED MONTE CARLO METHOD TO SOLVE NON-LINEAR OPTIMIZATION PROBLEMS

Masaaki Taguri

1975 年 5 巻 2 号 p. 65-76
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.65

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ON MONETARY INTEREST FROM A PROBABILISTIC POINT OF VIEW

Ryoichiro Sato

1975 年 5 巻 2 号 p. 77-85
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.77

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A new approach is made to the theory of monetary interest from a point of view of probability theory.

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多変量解析における検定統計量の一般分布にたいする漸近展開

最近の発展にみられる諸方法の概説 I

塩谷実

1975 年 5 巻 2 号 p. 87-103
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.87

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This is a survey paper on various methods developed in recent years for obtaining asymptotic expansions for the nonnull distributions of multivariate test statistics. In Part I, two methods are discussed: (1) one by the Taylor expansion, including studentization; (2) one by the expansion of the exact characteristic functions using the formulae for weighted sums of zonal polynomials. Part II will be given in the separate paper in the next issue, and contain (3) the method based on the system of partial differential equations satisfied by the hypergeometric functions, (4) the method by an expansion of test statistics in terms of normal variates, and (5) the method based on the representation of an orthogonal matrix by a skew symmetric matrix. In the discussion, emphasis is on the basic idea of the deriving techniques, and details of computation and final forms of individual asymptotic expansions explained as examples to clarify the idea are omitted; appropriate references, however, are given.

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大気汚染をめぐるデータ解析の話題

柳本武美

1975 年 5 巻 2 号 p. 105-117
発行日: 1975年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.5.105

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