{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T03:25:59Z","timestamp":1771125959359,"version":"3.50.1"},"reference-count":26,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Statistics bureaus around the world have been faced with an increasing need to provide reliable estimates of economic and social indices, such as proportions or rates, from socioeconomic survey data at small area levels. For example, in 2015, the Member States of the United Nations committed themselves to the 2030 Agenda for Sustainable Development Goals, which requires the national statistical offices and other government agencies of the Member States to provide high-quality, timely, and reliable national indicators at a disaggregated level. However, due to the relatively small sample size of these areas or domains, it is not viable to obtain estimates with an acceptable level of accuracy without using model-based approaches. Here, we propose to model the direct estimator of the rates or proportions in small area domains as being beta distributed. The novelty is that we also model the sampling precision estimator as a beta prime distribution. An evaluation study with real data shows that there is an additional gain in jointly modeling the direct estimator and its sampling precision estimator. An application is also provided to estimate the food insecurity index in small areas of a Brazilian state.<\/jats:p>","DOI":"10.1093\/jssam\/smaf002","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T22:10:06Z","timestamp":1741126206000},"source":"Crossref","is-referenced-by-count":1,"title":["A Beta\u2013Beta Prime Model for Rates and their Precision for Small Area Estimation: An Application to Brazilian Food Insecurity Index"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3880-4675","authenticated-orcid":false,"given":"Fernando A S","family":"Moura","sequence":"first","affiliation":[{"name":"Statistics Department of the Federal University of Rio de Janeiro Retired Professor in the , Ilha do Fund\u00e3o, Rio de Janeiro 21941-909, Brasil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7336-1320","authenticated-orcid":false,"given":"Soraia","family":"Pereira","sequence":"additional","affiliation":[{"name":"Researcher at the Centre for Statistics and Applications, University of Lisbon (CEAUL) and Assistant Professor in the Department of Mathematics, University of Minho, Campus de Azur\u00e9m, 4800-058 Guimar\u00e3es,","place":["Portugal"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7434-2383","authenticated-orcid":false,"given":"Giovani L","family":"Silva","sequence":"additional","affiliation":[{"name":"Researcher at the Centre for Statistics and Applications (CEAUL) and Assistant Professor in the Department of Mathematics, Instituto Superior T\u00e9cnico (IST), University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisbon,","place":["Portugal"]}]}],"member":"286","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"2025030422095298000_smaf002-B1","doi-asserted-by":"crossref","DOI":"10.1017\/9781108646185","volume-title":"Computational Bayesian Statistics: An Introduction","author":"Amaral Turkman","year":"2019"},{"key":"2025030422095298000_smaf002-B2","doi-asserted-by":"publisher","author":"Betancourt","year":"2013","DOI":"10.48550\/arXiv.1312.0906"},{"key":"2025030422095298000_smaf002-B3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s40300-021-00203-y","article-title":"A New Regression Model for Positive Random Variables with Skewed and Long Tail","volume":"79","author":"Bourguignon","year":"2021","journal-title":"Metron"},{"key":"2025030422095298000_smaf002-B4","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1093\/biomet\/46.3-4.477","article-title":"A Note on the Application of Quenouille\u2019s Method of Bias Reduction to the Estimation of Ratios","volume":"46","author":"Durbin","year":"1959","journal-title":"Biometrika"},{"key":"2025030422095298000_smaf002-B5","doi-asserted-by":"publisher","author":"FAO, IFAD, UNICEF, WFP and WHO","year":"2021","DOI":"10.4060\/cb4474en"},{"key":"2025030422095298000_smaf002-B6","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1080\/0266476042000214501","article-title":"Beta Regression for Modelling Rates and Proportions","volume":"31","author":"Ferrari","year":"2004","journal-title":"Journal of Applied Statistics"},{"key":"2025030422095298000_smaf002-B7","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1016\/j.csda.2011.07.005","article-title":"Small Area Estimation Using Skew Normal Models","volume":"56","author":"Ferraz","year":"2012","journal-title":"Computational Statistics & Data Analysis"},{"key":"2025030422095298000_smaf002-B8","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1111\/insr.12556","article-title":"A Spatial Variance-Smoothing Area Level Model for Small Area Estimation of Demographic Rates","volume":"91","author":"Gao","year":"2023","journal-title":"International Statistical Review"},{"key":"2025030422095298000_smaf002-B9","doi-asserted-by":"crossref","first-page":"2264","DOI":"10.1080\/03610926.2019.1570266","article-title":"Properties of the Beta Regression Model for Small Area Estimation of Proportions and Application to Estimation of Poverty Rates","volume":"49","author":"Janicki","year":"2020","journal-title":"Communications in Statistics - 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