{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T07:39:35Z","timestamp":1790321975443,"version":"4.1.0"},"reference-count":8,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[1971,7,1]],"date-time":"1971-07-01T00:00:00Z","timestamp":47174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1971,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Choi and Bulgren's (1968) estimator for the mixing measure of a mixture of known distributions is biased in small samples; a variant of their estimator has a much smaller bias, and a smaller mean squared error, for mixtures of normal distributions differing in mean. The maximum-likelihood estimator is shown to be more computable than Choi and Bulgren suggest. Estimation is much more difficult when the component distributions are unknown; for example, a mixture of two normal components has five parameters, but no more than four may be estimated when the components are close together.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1971.tb00884.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:23:33Z","timestamp":1544160213000},"page":"326-329","source":"Crossref","is-referenced-by-count":159,"title":["Comments and Queries Comment on \u201cAn Estimation Procedure for Mixtures of Distributions\u201d by Choi and Bulgren"],"prefix":"10.1093","volume":"33","author":[{"given":"P. D. M.","family":"Macdonald","sequence":"first","affiliation":[{"name":"Department of Biomathematics, University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920465306100_rssb00884-cit-0001","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/217195b0","article-title":"\u201cLeast-squares\u201d estimation of distribution mixtures","volume":"217","author":"Bartlett","year":"1968","journal-title":"Nature, Lond."},{"key":"2024090920465306100_rssb00884-cit-0002","first-page":"351","article-title":"Mixtures of discrete distributions","volume-title":"Classical and Contagious Discrete Distributions","author":"Buschke","year":"1965"},{"key":"2024090920465306100_rssb00884-cit-0003","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1214\/aoms\/1177699607","article-title":"On the estimation of mixing distributions","volume":"37","author":"Boes","year":"1966","journal-title":"Ann. Math. Statist."},{"key":"2024090920465306100_rssb00884-cit-0004","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1214\/aoms\/1177732758","article-title":"On sampling from compound populations","volume":"4","author":"Brown","year":"1933","journal-title":"Ann. Math. Statist."},{"key":"2024090920465306100_rssb00884-cit-0005","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1111\/j.2517-6161.1968.tb00743.x","article-title":"An estimation procedure for mixtures of distributions","volume":"30","author":"Choi","year":"1968","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090920465306100_rssb00884-cit-0006","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1093\/biomet\/56.3.463","article-title":"Estimating the components of a mixture of normal distributions","volume":"56","author":"Day","year":"1969","journal-title":"Biometrika"},{"key":"2024090920465306100_rssb00884-cit-0007","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1080\/01621459.1963.10480678","article-title":"Information for estimating the proportions in mixtures of exponential and normal distributions","volume":"58","author":"Hill","year":"1963","journal-title":"J. Amer. Statist. Ass."},{"key":"2024090920465306100_rssb00884-cit-0008","article-title":"FORTRAN programs for statistical estimation of distribution mixtures: some techniques for statistical analysis of length-frequency data","volume-title":"Fish. Res. Bd Canada","author":"Macdonald","year":"1969"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1971.tb00884.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/33\/2\/326\/49098858\/jrsssb_33_2_326.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/33\/2\/326\/49098858\/jrsssb_33_2_326.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T20:58:15Z","timestamp":1725915495000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/33\/2\/326\/7027118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1971,7,1]]},"references-count":8,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1971,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1971.tb00884.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1971,7]]},"published":{"date-parts":[[1971,7,1]]}}}