{"id":25370,"date":"2026-06-26T16:42:10","date_gmt":"2026-06-26T08:42:10","guid":{"rendered":"https:\/\/cde.nus.edu.sg\/isem\/?p=25370"},"modified":"2026-06-26T16:44:04","modified_gmt":"2026-06-26T08:44:04","slug":"novel-closed-form-point-estimators","status":"publish","type":"post","link":"https:\/\/cde.nus.edu.sg\/isem\/2026\/06\/novel-closed-form-point-estimators\/","title":{"rendered":"Novel Closed-Form Point Estimators for the Beta Distribution"},"content":{"rendered":"\n<h2>\n\t\tISEM Seminar Series\n\t<\/h2>\n\t<table>\n<tbody>\n<tr>\n<td>\n<h2>&#8220;<strong>Novel Closed-Form Point Estimators for the Beta Distribution<\/strong>&#8220;<\/h2>\n<p><em>by<\/em><\/p>\n<strong>Dr Xun Xiao<\/strong>\n<strong>Senior Lecturer<\/strong>\n<p>Department of Mathematics and Statistics, University of Otago<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>29 June 2026 (Monday), 4pm &#8211; 5pm<br \/>\nVenue: E1-07-21\/22 &#8211; ISEM Executive Classroom<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t<table>\n<tbody>\n<tr>\n<td width=\"765\">ABSTRACT\n<p>In this talk, we discuss and investigate novel closed-form point estimators for the beta distribution. The estimators of the first type are a modified version of Pearson&#8217;s method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments, in the moment estimation equations and solve the mixed-type moment equations simultaneously. The estimators of the second type are based on an approximation to Fisher&#8217;s likelihood principle. The idea is to solve two score equations derived from the log-likelihood function of generalized beta distributions. Both resulting estimators are in closed forms, strongly consistent, and asymptotically normal. In addition, through theoretical analyses and extensive simulations, the proposed estimators are shown to perform very close to the maximum likelihood estimators in both small and large samples, and they significantly outperform the method of moment estimators.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"765\">Dr. Xun Xiao is currently a Senior Lecturer in the Department of Mathematics and Statistics at the University of Otago, New Zealand. He received his B.Sc in Statistics from the University of Science and Technology of China in 2011 and his Ph.D. degree from the Department of Systems Engineering and Engineering Management at City University of Hong Kong in 2016. His current research focuses on industrial statistics and point process modelling.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n","protected":false},"excerpt":{"rendered":"<p>by Dr Xun Xiao<\/p>\n<p>Senior Lecturer <\/p>\n<p>Department of Mathematics and Statistics, University of Otago<\/p>\n<p>29 June 2026<\/p>\n","protected":false},"author":310,"featured_media":25372,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[35,1],"tags":[40],"class_list":["post-25370","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-seminars","category-uncategorized","tag-professional"],"acf":[],"_links":{"self":[{"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/posts\/25370","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/users\/310"}],"replies":[{"embeddable":true,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/comments?post=25370"}],"version-history":[{"count":2,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/posts\/25370\/revisions"}],"predecessor-version":[{"id":25376,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/posts\/25370\/revisions\/25376"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/media\/25372"}],"wp:attachment":[{"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/media?parent=25370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/categories?post=25370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cde.nus.edu.sg\/isem\/wp-json\/wp\/v2\/tags?post=25370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}