{"id":2750,"date":"2024-11-16T19:00:41","date_gmt":"2024-11-16T11:00:41","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2750"},"modified":"2024-12-20T20:46:43","modified_gmt":"2024-12-20T12:46:43","slug":"zhou-wei-ling-c-2016-higher-order-expansions-of-powered-extremes-of-normal-samples-statistics-and-probability-letters-vol-111-pp-12-17","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/en\/publications-en\/publications-all-en\/2750\/","title":{"rendered":"Zhou, W., &#038; Ling, C. (2016). Higher-order expansions of powered extremes of normal samples. Statistics &#038; Probability Letters, 111, 12-17."},"content":{"rendered":"<p>In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions\/densities of normalized extremes depends in principle on the power index.<\/p>\r\n\r\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" style=\"width: 100%; height: 600px;\" data=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/\u5468\u73ae-Ling-C.-2016.-Higher-order-expansions-of-powered-extremes-of-normal-samples-Statistics-and-Probability-Letters-Vol.-111-pp.-12-17.pdf\" type=\"application\/pdf\" width=\"300\" height=\"150\" aria-label=\"\u5d4c\u5165 &lt;strong&gt;&lt;mark style=&quot;background-color:rgba(0, 0, 0, 0)&quot; class=&quot;has-inline-color has-vivid-cyan-blue-color&quot;&gt;Higher-order expansions of powered extremes of normal samples, Statistics and Probability Letters, Vol. 111, pp. 12-17.pdf&lt;\/mark&gt;&lt;\/strong&gt;\"><\/object><a id=\"wp-block-file--media-2ad01960-43a5-4dd5-bd14-78de744cf164\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/\u5468\u73ae-Ling-C.-2016.-Higher-order-expansions-of-powered-extremes-of-normal-samples-Statistics-and-Probability-Letters-Vol.-111-pp.-12-17.pdf\"><strong><mark class=\"has-inline-color has-vivid-cyan-blue-color\" style=\"background-color: rgba(0, 0, 0, 0);\">Higher-order expansions of powered extremes of normal samples, Statistics and Probability Letters, Vol. 111, pp. 12-17.pdf<\/mark><\/strong><\/a><a class=\"wp-block-file__button wp-element-button\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/\u5468\u73ae-Ling-C.-2016.-Higher-order-expansions-of-powered-extremes-of-normal-samples-Statistics-and-Probability-Letters-Vol.-111-pp.-12-17.pdf\" download=\"\" aria-describedby=\"wp-block-file--media-2ad01960-43a5-4dd5-bd14-78de744cf164\">Download<\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions\/densities of normalized extremes depends in principle on the power index.<\/p>\n","protected":false},"author":1,"featured_media":2747,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[21],"tags":[],"class_list":["post-2750","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-all-en"],"acf":[],"lang":"en","translations":{"en":2750,"cn":2583},"pll_sync_post":[],"_links":{"self":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2750"}],"version-history":[{"count":3,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2750\/revisions"}],"predecessor-version":[{"id":3557,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2750\/revisions\/3557"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media\/2747"}],"wp:attachment":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}