{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:47:59Z","timestamp":1759117679114},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:p> Assume that [Formula: see text] mobile sensors are thrown uniformly and independently at random with the uniform distribution on the unit interval. We study the expected sum over all sensors [Formula: see text] from [Formula: see text] to [Formula: see text] where the contribution of the [Formula: see text] sensor is its displacement from the current location to the anchor equidistant point [Formula: see text] raised to the [Formula: see text] power, when [Formula: see text] is an odd natural number. <\/jats:p><jats:p> As a consequence, we derive the following asymptotic identity. Fix [Formula: see text] positive integer. Let [Formula: see text] denote the [Formula: see text] order statistic from a random sample of size [Formula: see text] from the Uniform[Formula: see text] population. Then [Formula: see text] where [Formula: see text] is the Gamma function. <\/jats:p>","DOI":"10.1142\/s1793830919500150","type":"journal-article","created":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T02:08:12Z","timestamp":1544753292000},"page":"1950015","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotic formula for sum of moment mean deviation for order statistics from uniform distribution"],"prefix":"10.1142","volume":"11","author":[{"given":"Rafa\u0142","family":"Kapelko","sequence":"first","affiliation":[{"name":"Department of Computer Science, Faculty of Fundamental Problems of Technology, Wroc\u0142aw University of Science and Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370 Wroc\u0142aw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2019,4,24]]},"reference":[{"key":"S1793830919500150BIB001","volume-title":"A First Course in Order Statistics","volume":"54","author":"Arnold B.","year":"1992"},{"key":"S1793830919500150BIB002","volume-title":"An Introduction to Probability Theory and its Applications","volume":"1","author":"Feller W.","year":"1968"},{"key":"S1793830919500150BIB003","volume-title":"An Introduction to the Analysis of Algorithms","author":"Flajolet P.","year":"1995"},{"key":"S1793830919500150BIB004","volume-title":"Combinatorial Identities for Stirling Numbers","author":"Gould H.","year":"2015"},{"key":"S1793830919500150BIB005","volume-title":"Concrete Mathematics A Foundation for Computer Science","author":"Graham R.","year":"1994"},{"key":"S1793830919500150BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2016.06.004"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500150","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:29:44Z","timestamp":1565119784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2019,4,24]]},"published-print":{"date-parts":[[2019,4]]}},"alternative-id":["10.1142\/S1793830919500150"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500150","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4]]}}}