{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T05:23:05Z","timestamp":1761110585850,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:00:00Z","timestamp":1622592000000},"content-version":"vor","delay-in-days":152,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.<\/jats:p>","DOI":"10.1155\/2021\/5273191","type":"journal-article","created":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T21:37:57Z","timestamp":1622669877000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2255-1167","authenticated-orcid":false,"given":"Fuad S.","family":"Al-Duais","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4090-6125","authenticated-orcid":false,"given":"Mohammed","family":"Alhagyan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,6,2]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"75","article-title":"Estimations in step-partially accelerated life tests for an exponential lifetime model under progressive type-I censoring and general entropy loss function","author":"Abdel-Hamid A. H.","year":"2016","journal-title":"Journal of Mathematics and Statistical Science"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.18187\/pjsor.v16i1.2854"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.4236\/ojs.2020.101004"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2018.1541170"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym11121463"},{"key":"e_1_2_9_6_2","unstructured":"EllahA. H. A. Bayesian and non-Bayesian estimation of the inverse Weibull model based on generalized order statistics 2012 4b."},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-016-0787-2"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.17654\/adasapr2015_001_027"},{"key":"e_1_2_9_9_2","first-page":"15","article-title":"Some distributional properties and estimation of parameters for inverse Rayleigh distribution through lower record values","volume":"2","author":"Muhammad M.","year":"2007","journal-title":"International Journal of Statistics and Systems"},{"key":"e_1_2_9_10_2","first-page":"985","article-title":"Estimations and prediction from the inverse Rayleigh model based on lower record statistics","volume":"9","author":"Shawky A. I.","year":"2012","journal-title":"Life Science Journal"},{"key":"e_1_2_9_11_2","first-page":"3057","article-title":"Estimation and prediction from inverse Rayleigh distribution based on lower record values","volume":"4","author":"Soliman A.","year":"2010","journal-title":"Applied Mathematical Sciences"},{"key":"e_1_2_9_12_2","first-page":"1","article-title":"Estimation of inverse Rayleigh distribution parameters for type II singly and doubly censored data based on lower record values","volume":"7","author":"Manzoor S.","year":"2018","journal-title":"International Journal of Probability and Statistics"},{"key":"e_1_2_9_13_2","first-page":"18","article-title":"Bayes estimator for inverse Rayleigh distribution under generalized weighted loss function","volume":"3","author":"Rasheed H. A.","year":"2017","journal-title":"Mathematics and Statistics Journal"},{"key":"e_1_2_9_14_2","first-page":"8","article-title":"Bayesian approach in estimation of scale parameter of inverse Rayleigh distribution","volume":"2","author":"Abdullah H.","year":"2016","journal-title":"Mathematics and Statistics Journal"},{"key":"e_1_2_9_15_2","first-page":"195","article-title":"A Bayesian approach to real estate assessment","author":"Varian H. R.","year":"1975","journal-title":"Studies in Bayesian Econometric and Statistics in Honor of Leonard J. Savage"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-010-0307-8"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2008.07.008"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1986.10478289"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1080\/16843703.2008.11673408"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5273191.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5273191.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/5273191","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T23:24:17Z","timestamp":1723245857000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/5273191"}},"subtitle":[],"editor":[{"given":"Ahmed Mostafa","family":"Khalil","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/5273191"],"URL":"https:\/\/doi.org\/10.1155\/2021\/5273191","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-04-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-24","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-02","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5273191"}}