{"id":297,"date":"2017-04-24T12:27:06","date_gmt":"2017-04-24T12:27:06","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=297"},"modified":"2017-04-24T12:27:14","modified_gmt":"2017-04-24T12:27:14","slug":"mathematical-methods-constructing-generalizations-skew-normal-distributions","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/","title":{"rendered":"Mathematical Methods of constructing Generalizations Skew Normal Distributions"},"content":{"rendered":"<p>In this paper, two different mathematical methods are used to derive skew distributions.<br \/>\nThe results generalize Azzalini (1985) and Fern\u00b4andez and Steel (1998) skew distributions<br \/>\ngenerating new results in general, and skew normal distribution in particular. Some mathematical<br \/>\nproperties, such as n-th moments, distribution function, moments generating function,<br \/>\nare also given for the generalizations. Some known and new special cases are also<br \/>\nmentioned. Some graphs for skew distributions are included. Results are applied to two<br \/>\npractical problems. Shannon and Renyi entropies as well as Fisher information are also<br \/>\nobtained.<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/45n1_2.pdf\">45n1_2<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, two different mathematical methods are used to derive skew distributions. The results generalize Azzalini (1985) and Fern\u00b4andez and Steel (1998) skew distributions generating new results in general, and skew normal distribution in particular. Some mathematical properties, such as n-th moments, distribution function, moments generating function, are also given for the generalizations. Some [&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":[9],"issuem_issue_categories":[],"issuem_issue_tags":[],"class_list":["post-297","article","type-article","status-publish","format-standard","hentry","issuem_issue-v45n1"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mathematical Methods of constructing Generalizations Skew Normal Distributions - 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\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematical Methods of constructing Generalizations Skew Normal Distributions - JSR\" \/>\n<meta property=\"og:description\" content=\"In this paper, two different mathematical methods are used to derive skew distributions. The results generalize Azzalini (1985) and Fern\u00b4andez and Steel (1998) skew distributions generating new results in general, and skew normal distribution in particular. Some mathematical properties, such as n-th moments, distribution function, moments generating function, are also given for the generalizations. Some [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2017-04-24T12:27:14+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/\",\"name\":\"Mathematical Methods of constructing Generalizations Skew Normal Distributions - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2017-04-24T12:27:06+00:00\",\"dateModified\":\"2017-04-24T12:27:14+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/jsr.isrt.ac.bd\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Articles\",\"item\":\"https:\/\/jsr.isrt.ac.bd\/article\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Mathematical Methods of constructing Generalizations Skew Normal Distributions\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/\",\"name\":\"JSR\",\"description\":\"Journal of Statistical Research\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/jsr.isrt.ac.bd\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Mathematical Methods of constructing Generalizations Skew Normal Distributions - JSR","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/","og_locale":"en_US","og_type":"article","og_title":"Mathematical Methods of constructing Generalizations Skew Normal Distributions - JSR","og_description":"In this paper, two different mathematical methods are used to derive skew distributions. The results generalize Azzalini (1985) and Fern\u00b4andez and Steel (1998) skew distributions generating new results in general, and skew normal distribution in particular. Some mathematical properties, such as n-th moments, distribution function, moments generating function, are also given for the generalizations. Some [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/","og_site_name":"JSR","article_modified_time":"2017-04-24T12:27:14+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/","name":"Mathematical Methods of constructing Generalizations Skew Normal Distributions - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2017-04-24T12:27:06+00:00","dateModified":"2017-04-24T12:27:14+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/mathematical-methods-constructing-generalizations-skew-normal-distributions\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/jsr.isrt.ac.bd\/"},{"@type":"ListItem","position":2,"name":"Articles","item":"https:\/\/jsr.isrt.ac.bd\/article\/"},{"@type":"ListItem","position":3,"name":"Mathematical Methods of constructing Generalizations Skew Normal Distributions"}]},{"@type":"WebSite","@id":"https:\/\/jsr.isrt.ac.bd\/#website","url":"https:\/\/jsr.isrt.ac.bd\/","name":"JSR","description":"Journal of Statistical Research","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/jsr.isrt.ac.bd\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"}]}},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article"}],"about":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/comments?post=297"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/297\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=297"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=297"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=297"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}