{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T21:10:36Z","timestamp":1780089036089,"version":"3.54.0"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T00:00:00Z","timestamp":1590624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research","award":["RG-2-150-37"],"award-info":[{"award-number":["RG-2-150-37"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the R\u00e9nyi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of R\u00e9nyi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.<\/jats:p>","DOI":"10.3390\/e22060601","type":"journal-article","created":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T08:27:48Z","timestamp":1590654468000},"page":"601","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data"],"prefix":"10.3390","volume":"22","author":[{"given":"Rashad A. R.","family":"Bantan","sequence":"first","affiliation":[{"name":"Department of Marine Geology, Faculty of Marine Sience, King AbdulAziz University, Jeddah 21551, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e9 de Caen, LMNO, Campus II, Science 3, 14032 Caen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-9890","authenticated-orcid":false,"given":"Farrukh","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63100, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Amigo, J.M., Balogh, S.G., and Hernandez, S. (2018). A brief review of generalized entropies. Entropy, 20.","DOI":"10.3390\/e20110813"},{"key":"ref_3","unstructured":"R\u00e9nyi, A. (1961). On measures of entropy and information. 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