{"id":596,"date":"2017-09-28T04:46:51","date_gmt":"2017-09-28T04:46:51","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=596"},"modified":"2017-09-28T04:47:37","modified_gmt":"2017-09-28T04:47:37","slug":"approximating-cumulative-distribution-function-normal-distribution","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/","title":{"rendered":"Approximating the cumulative distribution function of the normal distribution"},"content":{"rendered":"<p>Over the years, a number of approximations to the cdf of the Normal distribution<br \/>\nhave been proposed. How does one make a choice among them? This paper<br \/>\ncompares their performance with a view to identifying the best among them.<br \/>\nOur analysis reveals that a uniformly best approximation formula does not exist.<br \/>\nLocally best are identi\fed. Finally we combine the locally best approximations to<br \/>\nobtain a combined formula with a very high accuracy. A subroutine is presented.<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/41n1_5.pdf\">Fulltext<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Over the years, a number of approximations to the cdf of the Normal distribution have been proposed. How does one make a choice among them? This paper compares their performance with a view to identifying the best among them. Our analysis reveals that a uniformly best approximation formula does not exist. Locally best are identi\fed. [&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":[18],"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>Approximating the cumulative distribution function of the normal distribution - 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\/approximating-cumulative-distribution-function-normal-distribution\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Approximating the cumulative distribution function of the normal distribution - JSR\" \/>\n<meta property=\"og:description\" content=\"Over the years, a number of approximations to the cdf of the Normal distribution have been proposed. How does one make a choice among them? This paper compares their performance with a view to identifying the best among them. Our analysis reveals that a uniformly best approximation formula does not exist. Locally best are identi ed. [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28T04:47:37+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\/approximating-cumulative-distribution-function-normal-distribution\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/\",\"name\":\"Approximating the cumulative distribution function of the normal distribution - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2017-09-28T04:46:51+00:00\",\"dateModified\":\"2017-09-28T04:47:37+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/#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\":\"Approximating the cumulative distribution function of the normal distribution\"}]},{\"@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":"Approximating the cumulative distribution function of the normal distribution - 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\/approximating-cumulative-distribution-function-normal-distribution\/","og_locale":"en_US","og_type":"article","og_title":"Approximating the cumulative distribution function of the normal distribution - JSR","og_description":"Over the years, a number of approximations to the cdf of the Normal distribution have been proposed. How does one make a choice among them? This paper compares their performance with a view to identifying the best among them. Our analysis reveals that a uniformly best approximation formula does not exist. Locally best are identi ed. [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/","og_site_name":"JSR","article_modified_time":"2017-09-28T04:47:37+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/","name":"Approximating the cumulative distribution function of the normal distribution - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2017-09-28T04:46:51+00:00","dateModified":"2017-09-28T04:47:37+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/approximating-cumulative-distribution-function-normal-distribution\/#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":"Approximating the cumulative distribution function of the normal distribution"}]},{"@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\/596"}],"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=596"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/596\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=596"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=596"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=596"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}