{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:27:36Z","timestamp":1771673256553,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T00:00:00Z","timestamp":1681171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project, King Saud University","award":["RSP2022R156"],"award-info":[{"award-number":["RSP2022R156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Over the last few decades, the statisticians and reliability analysts have looked at putting exponentiality to the test using the Laplace transform technique. The non-parametric statistical test used in this study, which is based on this technique, evaluates various treatment modalities by looking at failure behavior in the survival data that were gathered. Following use of the suggested strategy, patient survival times are recorded. In this investigation, it was presupposed that the Laplace transform order of (UBAC2) attribute or the constant failure rate would determine how the observed data behave (exponential scenario). If the survival data are exponential, the recommended treatment approach is ineffective. If the survival data are UBAC2L, the technique in use produces a better or a higher expected total present value than an older one governed by an exponential survival function (discussed in the Applications section). The efficiency and critical values of the test are calculated and compared to those of other tests in order to ensure that the suggested statistical test is applied correctly.<\/jats:p>","DOI":"10.3390\/axioms12040369","type":"journal-article","created":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T02:08:11Z","timestamp":1681265291000},"page":"369","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Non-Parametric Hypothesis Testing for Unknown Aged Class of Life Distribution Using Real Medical Data"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3493-033X","authenticated-orcid":false,"given":"Mahmoud. E.","family":"Bakr","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2189-2629","authenticated-orcid":false,"given":"Abdulhakim","family":"A. Al-Babtain","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,11]]},"reference":[{"key":"ref_1","unstructured":"Barlow, R.E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models, Hold, Reinhart and Wiston, Inc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"748","DOI":"10.2307\/3214012","article-title":"Aspects of positive aging","volume":"23","author":"Deshpande","year":"1986","journal-title":"J. Appl. Probab."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1002\/nav.3800290213","article-title":"The HNBUE and HNWUE classes of life distribution","volume":"29","author":"Klefsjo","year":"1982","journal-title":"Naval Res. Logist."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.spl.2004.06.029","article-title":"Some properties of classes of life distributions with unknown age","volume":"9","author":"Ahmad","year":"2004","journal-title":"Stat. Probab. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1520\/JTE20160501","article-title":"On the Properties of the UBAC(2) Class of Life Distributions","volume":"46","author":"Ali","year":"2018","journal-title":"J. Test. Eval."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"355","DOI":"10.18576\/isl\/110206","article-title":"A New Class of Life Distribution based on Laplace Transform and It\u2019s Applications","volume":"11","year":"2022","journal-title":"Inf. Sci. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0378-3758(00)00139-7","article-title":"Moments inequalities of aging families with hypotheses testing applications","volume":"92","author":"Ahmad","year":"2001","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_8","first-page":"266","article-title":"Mean residual life","volume":"4","author":"Rolski","year":"1975","journal-title":"Bull. Int. Stat. Inst."},{"key":"ref_9","first-page":"27","article-title":"On testing exponentiality against HNRBUE based on a goodness of fit","volume":"8","author":"Mahmoud","year":"2007","journal-title":"Int. J. Rel. Appl."},{"key":"ref_10","first-page":"4576","article-title":"Non-parametric testing for unknown age (UBAL) class of life distribution","volume":"48","author":"Ali","year":"2019","journal-title":"J. Test. Eval."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1080\/03610926.2018.1528370","article-title":"A new test for exponentiality against HNBUE alternatives","volume":"49","author":"Ghosh","year":"2020","journal-title":"Commun. Stat. Theor Meth."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"483","DOI":"10.21608\/joems.2018.2649.1035","article-title":"On NRBUL Class of Life Distributions","volume":"26","author":"Mahmoud","year":"2018","journal-title":"J. Egypt. Math. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1002\/asmb.2657","article-title":"Preservation of ILR and IFR aging classes in sums of dependent random variables","volume":"38","author":"Navarro","year":"2022","journal-title":"Appl. Stoch. Models Bus. Ind."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.spl.2018.02.005","article-title":"Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems","volume":"137","author":"Navarro","year":"2018","journal-title":"Stat. Probab. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"471","DOI":"10.18576\/jsap\/060302","article-title":"Testing EBUmgf Class of Life Distributions based on Laplace Transform Technique","volume":"6","author":"Gadallah","year":"2017","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"75","DOI":"10.18576\/jsap\/110106","article-title":"Characterizations and testing NBRUL class of life distributions based on Laplace transform technique","volume":"11","author":"Sadek","year":"2022","journal-title":"J. Stat. Appl. Probab."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1002\/qre.1557","article-title":"A new test for exponentiality versus NBUmgf life distribution based on Laplace transform","volume":"30","author":"Atallah","year":"2014","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_18","unstructured":"Lee, A.J. (1990). U-Statistics Theory and Practice, Marcel Dekker, Inc."},{"key":"ref_19","first-page":"81","article-title":"A goodness of fit approach to major life testing problems","volume":"2","author":"Ahmad","year":"2001","journal-title":"Int. J. Reliab. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1080\/00401706.1963.10490105","article-title":"Theoretical explanation of observed decreasing failure rate","volume":"5","author":"Proschan","year":"1963","journal-title":"Technometrics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"251","DOI":"10.2307\/1267788","article-title":"Inferences on the parameters of the Birnbaum-Saunders fatigue life distribution based on maximum likelihood estimation","volume":"23","author":"Engelhardt","year":"1981","journal-title":"Technometrics"},{"key":"ref_22","first-page":"1876073","article-title":"Bayesian Estimation of Gumbel Type-II Distribution under Type-II Censoring with Medical Applications","volume":"7","author":"Abbas","year":"2020","journal-title":"J. Comput. Math. Methods Med."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/4\/369\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:13:49Z","timestamp":1760123629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/4\/369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,11]]},"references-count":22,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["axioms12040369"],"URL":"https:\/\/doi.org\/10.3390\/axioms12040369","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,11]]}}}