{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T11:21:41Z","timestamp":1775128901784,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2012,1,31]],"date-time":"2012-01-31T00:00:00Z","timestamp":1327968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Multiply Type-II censored sampling arises in a life-testing experiment whenever the experimenter does not observe the failure times of some units placed on a life-test. In this paper, we obtain estimators for the entropy function of a double exponential distribution under multiply Type-II censored samples using the maximum likelihood estimation and the approximate maximum likelihood estimation procedures. We compare the proposed estimators in the sense of the mean squared errors by using Monte Carlo simulation.<\/jats:p>","DOI":"10.3390\/e14020161","type":"journal-article","created":{"date-parts":[[2012,1,31]],"date-time":"2012-01-31T11:06:27Z","timestamp":1328007987000},"page":"161-173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["An Estimation of the Entropy for a Double Exponential Distribution Based on Multiply Type-II Censored Samples"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6976-8518","authenticated-orcid":false,"given":"Suk-Bok","family":"Kang","sequence":"first","affiliation":[{"name":"Department of Statistics, Yeungnam University, Dae-dong, Gyongsan 712-749, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young-Seuk","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Statistics, Pusan National University, Geumjeong-gu, Busan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-Tae","family":"Han","sequence":"additional","affiliation":[{"name":"Informatization Team, Ministry of Patriots and Veterans Affairs, Yeouido-dong, Seoul 150-874, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinsoo","family":"Kim","sequence":"additional","affiliation":[{"name":"Senior Research Fellow, The Korea Institute for Health and Social Affairs, Bulgwangdong, Eunpyeonggu, Seoul 122-705, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. 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Reliab."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/757582647","article-title":"On the maximum likelihood estimation of the location and scale parameters of exponential distribution based on multiply Type-II censored samples","volume":"17","author":"Balakrishnan","year":"1990","journal-title":"J. Appl. Stat."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF02925325","article-title":"Estimation for one-parameter and two-parameter exponential distributions under multiple Type-II censoring","volume":"33","author":"Balasubramanian","year":"1992","journal-title":"Stat. Paper."},{"key":"ref_10","first-page":"69","article-title":"Approximate mle for the scale parameter of the double exponential distribution based on Type-II censored samples","volume":"33","author":"Kang","year":"1996","journal-title":"J. Kor. Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s001840000092","article-title":"Conditional inference procedures for the Laplace distribution when the observed samples are progressively censored","volume":"52","author":"Childs","year":"2000","journal-title":"Metrika"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/0094965031000105881","article-title":"Inference for the extreme value distribution under progressive Type-II censoring","volume":"74","author":"Balakrishnan","year":"2004","journal-title":"J. Stat. Comput. Simulat."},{"key":"ref_13","first-page":"603","article-title":"AMLEs for the exponential distribution based on multiple Type-II censored samples","volume":"12","author":"Kang","year":"2005","journal-title":"The Korean Communications in Statistics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1111\/j.2517-6161.1976.tb01566.x","article-title":"A test for normality based on sample entropy","volume":"38","author":"Vasicek","year":"1976","journal-title":"J. Roy. Stat. Soc. B Stat. Meth."},{"key":"ref_15","first-page":"61","article-title":"Estimating functionals related to a density by a class of statistics based on spacings","volume":"19","year":"1992","journal-title":"Scand. J. Stat."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Nevzorov, V.B. (2003). A Primer on Statistical Distribution, John Wiley & Sons.","DOI":"10.1002\/0471722227"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:41Z","timestamp":1760219321000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/2\/161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,31]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,2]]}},"alternative-id":["e14020161"],"URL":"https:\/\/doi.org\/10.3390\/e14020161","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,31]]}}}