{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T20:04:52Z","timestamp":1695499492531},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of <jats:italic>n<\/jats:italic> independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 at a rate of <jats:italic>n<\/jats:italic>\n               <jats:sup>-2\/3<\/jats:sup>. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and <jats:italic>n<\/jats:italic> is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.<\/jats:p>","DOI":"10.1017\/s0021900200011360","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:11Z","timestamp":1459263071000},"page":"466-482","source":"Crossref","is-referenced-by-count":2,"title":["Improved Approximation of the Sum of Random Vectors by the Skew Normal Distribution"],"prefix":"10.1017","volume":"51","author":[{"given":"Marcus C.","family":"Christiansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Loperfido","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S0021900200011360_ref38","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899352045"},{"key":"S0021900200011360_ref10","volume-title":"Normal Approximation and Asymptotic Expansions","year":"1986"},{"key":"S0021900200011360_ref37","first-page":"44","volume-title":"Pattern Recognition, 2004.","year":"2004"},{"key":"S0021900200011360_ref8","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/83.4.715"},{"key":"S0021900200011360_ref36","doi-asserted-by":"publisher","DOI":"10.1162\/0899766054323026"},{"key":"S0021900200011360_ref6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2005.00426.x"},{"key":"S0021900200011360_ref35","volume-title":"Encyclopedia of Statistical Sciences","year":"2006"},{"key":"S0021900200011360_ref5","first-page":"171","volume":"12","year":"1985","journal-title":"Scand. 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