{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T13:26:20Z","timestamp":1791293180445,"version":"4.1.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T00:00:00Z","timestamp":1363737600000},"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":[[2013,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log-concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.<\/jats:p>","DOI":"10.1111\/rssb.12011","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T13:14:15Z","timestamp":1363785255000},"page":"769-790","source":"Crossref","is-referenced-by-count":26,"title":["Asymptotics of the Discrete Log-Concave Maximum Likelihood Estimator and Related Applications"],"prefix":"10.1093","volume":"75","author":[{"given":"Fadoua","family":"Balabdaoui","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Dauphine , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanna","family":"Jankowski","sequence":"additional","affiliation":[{"name":"York University , Toronto, , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaspar","family":"Rufibach","sequence":"additional","affiliation":[{"name":"University of Zurich , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marios","family":"Pavlides","sequence":"additional","affiliation":[{"name":"Queen\u2019s University Belfast , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2013,3,20]]},"reference":[{"key":"2023031109461119500_","first-page":"17","article-title":"On the Poisson difference distribution inference and application","volume":"33","author":"Alzaid","year":"2010","journal-title":"Bull. 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