{"created":"2023-07-25T08:12:55.165638+00:00","id":13508,"links":{},"metadata":{"_buckets":{"deposit":"d825e45f-3839-4b59-8486-f1e2acfbfe55"},"_deposit":{"created_by":18,"id":"13508","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"13508"},"status":"published"},"_oai":{"id":"oai:ir.kagoshima-u.ac.jp:00013508","sets":["54:55"]},"author_link":["123998"],"item_5_date_6":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2017-03-31","subitem_date_issued_type":"Collected"}]},"item_5_date_granted_54":{"attribute_name":"学位授与年月日 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column カテゴリおよびlayer カテゴリ（層分類) の3 次元r×s× t 分割表についての研究である。本論文では、r × r 正方分割表において対称なセルの確率が等しいという対称性（symmetry) の帰無仮説のもとでの検定および、r × s× t 分割表における同時独立性（jointly independence) の帰無仮説のもとでの検定によるφ-ダイバージェンス統計量Cφ での帰無分布について考察する。パワーダイバージェンス統計量R^a は、統計量Cφ の特別な場合である。R^0 は対数尤度比統計量で、R^1 はピアソンのX^2 統計量である。また、a = 2/3 はCressie and Read [6] によって提唱された統計量である。これらの統計量は対称性の帰無仮説のもとでカイ二乗分布を極限分布として持っていることが知られている。また、この仮説のもとでCφ の分布に対する漸近展開にもとづく近似式の連続項を導出する。この連続項を使うことによって、Cφ の分布の新しい近似を提案する。さらに、その近似に基づき、Cφ のカイ二乗極限分布への収束速度の改良をした変換統計量を与える。また、R^a の場合の数値比較をすることによって、変換統計量が小標本に対してもよい近似となっていることを示す。","subitem_description_language":"ja","subitem_description_type":"Other"}]},"item_5_dissertation_number_55":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲理工研第441号"}]},"item_5_publisher_23":{"attribute_name":"公開者・出版者","attribute_value_mlt":[{"subitem_publisher":"鹿児島大学","subitem_publisher_language":"ja"},{"subitem_publisher":"Kagoshima 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