{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:41:42Z","timestamp":1773798102855,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper discusses the estimation and prediction problems for the Nadarajah-Haghighi distribution using progressive type-II censored samples. For the unknown parameters, we first calculate the maximum likelihood estimates through the Expectation\u2013Maximization algorithm. In order to choose the best Bayesian estimator, a loss function must be specified. When the loss is essentially symmetric, it is reasonable to use the square error loss function. However, for some estimation problems, the actual loss is often asymmetric. Therefore, we also need to choose an asymmetric loss function. Under the balanced squared error and symmetric squared error loss functions, the Tierney and Kadane method is used for calculating different kinds of approximate Bayesian estimates. The Metropolis-Hasting algorithm is also provided here. In addition, we construct a variety of interval estimations of the unknown parameters including asymptotic intervals, bootstrap intervals, and highest posterior density intervals using the sample derived from the Metropolis-Hasting algorithm. Furthermore, we compute the point predictions and predictive intervals for a future sample when facing the one-sample and two-sample situations. At last, we compare and appraise the performance of the provided techniques by carrying out a simulation study and analyzing a real rainfall data set.<\/jats:p>","DOI":"10.3390\/sym13060999","type":"journal-article","created":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T21:03:32Z","timestamp":1622754212000},"page":"999","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Estimation and Prediction for Nadarajah-Haghighi Distribution under Progressive Type-II Censoring"],"prefix":"10.3390","volume":"13","author":[{"given":"Mingjie","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4318-1780","authenticated-orcid":false,"given":"Wenhao","family":"Gui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"ref_1","unstructured":"Balakrishnan, N., and Cohen, A.C. 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