{"id":492,"date":"2017-09-24T05:53:54","date_gmt":"2017-09-24T05:53:54","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=492"},"modified":"2017-09-24T05:54:08","modified_gmt":"2017-09-24T05:54:08","slug":"note-construction-generalized-tukey-type-transformations","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/note-construction-generalized-tukey-type-transformations\/","title":{"rendered":"A note on the construction of generalized Tukey-type transformations"},"content":{"rendered":"<p>One possibility to construct heavy tail distributions is to directly manipulate a<br \/>\nstandard Gaussian random variable by means of transformations which satisfy<br \/>\ncertain conditions. This approach dates back to Tukey (1960) who introduces the<br \/>\npopular <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-604f84528aa51ac51424f48fc5396280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-transformation. Alternatively, the <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-b760ebc707e08dd6e1888ea8da4c2454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-transformation of MacGillivray<br \/>\n&amp; Cannon (1997) or the <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-bb8905e363b035a97b58399e113c48e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#74;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: 0px;\"\/>-transformation of Fischer &amp; Klein (2004) may be used.<br \/>\nRecently, Klein &amp; Fischer (2006) proposed a very general power kurtosis transformation<br \/>\nwhich includes the above-mentioned transformations as special cases.<br \/>\nUnfortunately, their transformation requires an in\fnite number of unknown parameters<br \/>\nto be estimated. In contrast, we introduce a very simple method to<br \/>\nconstruct exible kurtosis transformations. In particular, manageable &#8220;superstructures&#8221;<br \/>\nare suggested in order to statistically discriminate between <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-604f84528aa51ac51424f48fc5396280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-, <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-bb8905e363b035a97b58399e113c48e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#74;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: 0px;\"\/>&#8211; and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-b760ebc707e08dd6e1888ea8da4c2454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-distributions (associated to <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-604f84528aa51ac51424f48fc5396280_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-, <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-bb8905e363b035a97b58399e113c48e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#74;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: 0px;\"\/>&#8211; and <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-b760ebc707e08dd6e1888ea8da4c2454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#75;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>-transformations).<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/42n2_7.pdf\">Fulltext<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>One possibility to construct heavy tail distributions is to directly manipulate a standard Gaussian random variable by means of transformations which satisfy certain conditions. This approach dates back to Tukey (1960) who introduces the popular -transformation. Alternatively, the -transformation of MacGillivray &amp; Cannon (1997) or the -transformation of Fischer &amp; Klein (2004) may be used. [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"issuem_issue":[15],"issuem_issue_categories":[],"issuem_issue_tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A note on the construction of generalized Tukey-type transformations - JSR<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jsr.isrt.ac.bd\/article\/note-construction-generalized-tukey-type-transformations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A note on the construction of generalized Tukey-type transformations - JSR\" \/>\n<meta property=\"og:description\" content=\"One possibility to construct heavy tail distributions is to directly manipulate a standard Gaussian random variable by means of transformations which satisfy certain conditions. This approach dates back to Tukey (1960) who introduces the popular -transformation. Alternatively, the -transformation of MacGillivray &amp; Cannon (1997) or the -transformation of Fischer &amp; Klein (2004) may be used. 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This approach dates back to Tukey (1960) who introduces the popular -transformation. Alternatively, the -transformation of MacGillivray &amp; Cannon (1997) or the -transformation of Fischer &amp; Klein (2004) may be used. 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