{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T17:59:06Z","timestamp":1761674346243,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T00:00:00Z","timestamp":1667865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Qassim University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the moment inequalities for some aging distributions are derived based on a mathematical class entitled \u201ca new better than renewal used in Laplace transform order in increasing convex order class (NBRULC)\u201d. The introduced inequalities can be utilized as a new mathematical test for the exponentiality property versus NBRULC. If the mean life is finitely based on these inequalities, then all higher-order moments exist. Pitman\u2019s asymptotic efficiency of the new mathematical test is derived and studied in detail for some asymmetric probability models. The new mathematical test\u2019s power is estimated in reliability studies for a few well-known alternative asymmetric models. The problem in the case of right-censored data is also handled. After that, applying the suggested test to practical issues is demonstrated using asymmetric, real datasets.<\/jats:p>","DOI":"10.3390\/sym14112353","type":"journal-article","created":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T02:44:32Z","timestamp":1667961872000},"page":"2353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Moment Inequality for the NBRULC Class: Statistical Properties with Applications to Model Asymmetric Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afrah","family":"Al-Bossly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-3536","authenticated-orcid":false,"given":"Rashad M.","family":"EL-Sagheer","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt"},{"name":"High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bader","family":"Almohaimeed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Waleed B. H.","family":"Etman","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Artificial Intelligence, Modern University for Technology and Information, Cairo 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5619-210X","authenticated-orcid":false,"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Department of Mathematics, International Telematic University Uninettuno, 00186 Rome, Italy"},{"name":"Department of Statistics and Computer Sciences, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0378-3758(00)00139-7","article-title":"Moments inequalities of aging families of distributions with hypothesis testing applications","volume":"92","author":"Ahmad","year":"2001","journal-title":"J. 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