{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:49:51Z","timestamp":1761745791700,"version":"build-2065373602"},"reference-count":24,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,1,10]],"date-time":"2011-01-10T00:00:00Z","timestamp":1294617600000},"content-version":"vor","delay-in-days":708,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Brit J Math &amp;amp; Statis"],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p>\n                    This paper presents the asymptotic expansions of the distributions of the two\u2010sample\n                    <jats:italic>t<\/jats:italic>\n                    \u2010statistic and the Welch statistic, for testing the equality of the means of two independent populations under non\u2010normality. Unlike other approaches, we obtain the null distributions in terms of the distribution and density functions of the standard normal variable up to\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\u22121<\/jats:sup>\n                    , where\n                    <jats:italic>n<\/jats:italic>\n                    is the pooled sample size. Based on these expansions, monotone transformations are employed to remove the higher\u2010order cumulant effect. We show that the new statistics can improve the precision of statistical inference to the level of\n                    <jats:italic>o<\/jats:italic>\n                    (\n                    <jats:italic>n<\/jats:italic>\n                    <jats:sup>\u22121<\/jats:sup>\n                    ). Numerical studies are carried out to demonstrate the performance of the improved statistics. Some general rules for practitioners are also recommended.\n                  <\/jats:p>","DOI":"10.1348\/000711007x246246","type":"journal-article","created":{"date-parts":[[2008,1,23]],"date-time":"2008-01-23T22:20:58Z","timestamp":1201126858000},"page":"21-40","source":"Crossref","is-referenced-by-count":7,"title":["Improved statistics for contrasting means of two samples under non\u2010normality"],"prefix":"10.1111","volume":"62","author":[{"given":"Jin","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinping","family":"Cui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arjun K.","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,1,10]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1198\/000313001317098176"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02911638"},{"volume-title":"Normal approximation and asymptotic expansions","year":"1976","author":"Bhattacharya R. 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