{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,20]],"date-time":"2023-08-20T05:19:48Z","timestamp":1692508788867},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:p> If a message can have n different values and all values are equally probable, then the entropy of the message is log(n). In the present paper, we calculate the expectation value of the entropy, for arbitrary probability distribution. For that purpose, we assume \u2018the probability of a probability distribution\u2019 being uniformly distributed over Bhattacharyya's statistical space, i.e. the unitary n-dimensional hyperoctant. After some calculations, this turns out to amount to log(n) \u2212 [2 \u2212 log(2) \u2212 \u03b3] = log(n) \u2212 0.7297\u2026, where \u03b3 is Buler's constant. <\/jats:p>","DOI":"10.1023\/a:1015687824928","type":"journal-article","created":{"date-parts":[[2002,12,28]],"date-time":"2002-12-28T19:22:22Z","timestamp":1041103342000},"page":"97-113","source":"Crossref","is-referenced-by-count":3,"title":["The Expectation Value of the Entropy of a Digital Message"],"prefix":"10.1142","volume":"09","author":[{"given":"Alexis","family":"De Vos","sequence":"first","affiliation":[{"name":"Vakgroep voor elektronika en informatiesystemen, Universiteit Gent, Sint Pietersnieuwstraat 41, B\u20139000 Gent, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf1","first-page":"99","volume":"35","author":"Bhattacharyya A.","journal-title":"Bulletin of the Calcutta Mathematical Society"},{"key":"rf2","first-page":"345","volume":"43","author":"Atkinson C.","journal-title":"The Indian Journal of Statistics"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.23.357"},{"key":"rf4","first-page":"363","volume":"32","author":"Aherne F.","journal-title":"Kybernetika"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1286-7_11"},{"key":"rf6","volume-title":"An introduction to the geometry in n dimensions","author":"Sommerville D.","year":"1958"},{"key":"rf7","volume-title":"A course in the geometry of n dimensions","author":"Kendall M.","year":"1961"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-2323-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(92)90232-F"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(93)90386-I"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0079-6727(99)00002-6"},{"key":"rf13","unstructured":"I.\u00a0Gradshteyn and I.\u00a0Ryzhik, Table of integrals, series, and products (Academic Press, New York, 1980)\u00a0p. xliii, 336."},{"key":"rf14","unstructured":"I.\u00a0Gradshteyn and I.\u00a0Ryzhik, Table of integrals, series, and products, 5th edn. (Academic Press, Boston, 1994)\u00a0p. xlv, 381."}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1023\/A%3A1015687824928","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:35:45Z","timestamp":1565105745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1023\/A%3A1015687824928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":13,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2002,6]]}},"alternative-id":["10.1023\/A:1015687824928"],"URL":"https:\/\/doi.org\/10.1023\/a:1015687824928","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}