{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:49:01Z","timestamp":1776491341849,"version":"3.51.2"},"reference-count":26,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T00:00:00Z","timestamp":1701216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yunnan Key Laboratory of Modern Analytical Mathematics and Applications","award":["202302AN360007"],"award-info":[{"award-number":["202302AN360007"]}]},{"name":"Yunnan Key Laboratory of Modern Analytical Mathematics and Applications","award":["MTR\/2022\/000183"],"award-info":[{"award-number":["MTR\/2022\/000183"]}]},{"name":"Science and Engineering Research Board, India","award":["202302AN360007"],"award-info":[{"award-number":["202302AN360007"]}]},{"name":"Science and Engineering Research Board, India","award":["MTR\/2022\/000183"],"award-info":[{"award-number":["MTR\/2022\/000183"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, different estimation is discussed for a general family of inverse exponentiated distributions. Under the classical perspective, maximum likelihood and uniformly minimum variance unbiased are proposed for the model parameters. Based on informative and non-informative priors, various Bayes estimators of the shape parameter and reliability function are derived under different losses, including general entropy, squared-log error, and weighted squared-error loss functions as well as another new loss function. The behavior of the proposed estimators is evaluated through extensive simulation studies. Finally, two real-life datasets are analyzed from an illustration perspective.<\/jats:p>","DOI":"10.3390\/axioms12121096","type":"journal-article","created":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T12:01:00Z","timestamp":1701259260000},"page":"1096","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Comparison of Estimation Methods for Reliability Function for Family of Inverse Exponentiated Distributions under New Loss Function"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7719-1480","authenticated-orcid":false,"given":"Rani","family":"Kumari","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Patna, Patna 800005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9687-6036","authenticated-orcid":false,"given":"Yogesh Mani","family":"Tripathi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Bihta 801106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4342-2487","authenticated-orcid":false,"given":"Rajesh Kumar","family":"Sinha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Patna, Patna 800005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2600-5112","authenticated-orcid":false,"given":"Liang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Yunnan Normal University, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1080\/00949655.2012.696117","article-title":"Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data","volume":"84","author":"Ghitany","year":"2014","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1007\/s00362-016-0810-7","article-title":"Classical and Bayesian estimation of reliability in a multicomponent stressstrength model based on a general class of inverse exponentiated distributions","volume":"59","author":"Kizilaslan","year":"2018","journal-title":"Stat. Pap."},{"key":"ref_3","unstructured":"Fisher, A.J. (2016, December 12). Statistical Inferences of Rs,k = Pr(Xk\u2212s+1:k > Y) for General Class of Exponentiated Inverted Exponential Distribution with Progressively Type-II Censored Samples with Uniformly Distributed Random Removal. Available online: https:\/\/scholar.utc.edu\/theses\/493.2016."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1080\/16843703.2022.2125762","article-title":"Reliability estimation for the inverted exponentiated Pareto distribution","volume":"20","author":"Kumari","year":"2023","journal-title":"Qual. Technol. Quant. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Temraz, N.S.Y. (2023). Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution. PLoS ONE, 18.","DOI":"10.1371\/journal.pone.0280183"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"De la Cruz, R., Salinas, H.S., and Meza, C. (2022). Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution. Symmetry, 14.","DOI":"10.3390\/sym14040837"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Alsadat, N., Hassan, A.S., Elgarhy, M., Chesneau, C., and Mohamed, R.E. (2023). An efficient stress-strength reliability estimate of the unit gompertz distribution using ranked set sampling. Symmetry, 15.","DOI":"10.3390\/sym15051121"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"EL-Sagheer, R.M., Eliwa, M.S., El-Morshedy, M., Al-Essa, L.A., Al-Bossly, A., and Abd-El-Monem, A. (2023). Analysis of the stress-strength model using uniform truncated negative binomial distribution under progressive Type-II censoring. Axioms, 12.","DOI":"10.3390\/axioms12100949"},{"key":"ref_9","first-page":"617","article-title":"Type II general inverse exponential family of distributions","volume":"23","author":"Jamal","year":"2020","journal-title":"J. Stat. Manag. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"114934","DOI":"10.1016\/j.cam.2022.114934","article-title":"Inference for a general family of inverted exponentiated distributions under unified hybrid censoring with partially observed competing risks data","volume":"422","author":"Dutta","year":"2023","journal-title":"J. Comput. Appl. Math."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hashem, A.F., Alyami, S.A., and Yousef, M.M. (2023). Utilizing empirical Bayes estimation to assess reliability in inverted exponentiated Rayleigh distribution with progressive hybrid censored medical data. Axioms, 12.","DOI":"10.3390\/axioms12090872"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1080\/00949655.2018.1558225","article-title":"On progressively censored inverted exponentiated Rayleigh distribution","volume":"89","author":"Maurya","year":"2019","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_13","first-page":"315","article-title":"Pivotal inference for the inverted exponentiated Rayleigh distribution based on progressive Type-II censored data","volume":"39","author":"Gao","year":"2020","journal-title":"Am. J. Math. Manag. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"112969","DOI":"10.1016\/j.cam.2020.112969","article-title":"Inference for confidence sets of the generalized inverted exponential distribution under k-record values","volume":"380","author":"Wang","year":"2020","journal-title":"J. Comput. Appl. Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1109\/TR.1985.5222193","article-title":"Bayes estimation of the reliability function of normal distribution","volume":"34","author":"Sinha","year":"1985","journal-title":"IEEE Trans. Reliab."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0167-7152(86)90052-0","article-title":"Bayesian estimation of the reliability function of the inverse Gaussian distribution","volume":"4","author":"Sinha","year":"1986","journal-title":"Stat. Prob. Lett."},{"key":"ref_17","first-page":"47","article-title":"Bayes estimation of the reliability function and hazard rate of a weibull failure time distribution","volume":"1","author":"Sinha","year":"1986","journal-title":"Trab. Estad."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1109\/24.273598","article-title":"Bayes estimation of the extreme-value reliability function","volume":"42","author":"Lye","year":"1993","journal-title":"IEEE Trans. Reliab."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1109\/24.510807","article-title":"Bayes estimation of component-reliability from masked system-life data","volume":"45","author":"Lin","year":"1996","journal-title":"IEEE Trans. Reliab."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"127","DOI":"10.2307\/3315495","article-title":"Empirical Bayes estimation of reliability characteristics for an exponential family","volume":"27","author":"Pensky","year":"1999","journal-title":"Can. J. Stat."},{"key":"ref_21","first-page":"249","article-title":"Comparison of Bayes estimators of the parameter and reliability function for Rayleigh distribution under different loss functions","volume":"3","author":"Dey","year":"2009","journal-title":"Malay J. Math. Sci."},{"key":"ref_22","first-page":"113","article-title":"Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution","volume":"6","author":"Dey","year":"2012","journal-title":"Malay J. Math. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2595","DOI":"10.1080\/00949655.2021.1904239","article-title":"A comparison of estimation methods for reliability function of inverse generalized Weibull distribution under new loss function","volume":"91","author":"Amirzadi","year":"2021","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_24","unstructured":"Bader, M.G., and Priest, A.M. (1982). Progress in Science and Engineering Composites, ICCM-IV."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1016\/j.spl.2009.05.026","article-title":"Estimation of R = P(Y < X) for three-parameter Weibull distribution","volume":"79","author":"Kundu","year":"2009","journal-title":"Stat. Prob. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1023\/A:1011352923990","article-title":"Inference for reliability and stress-strength for a scaled Burr Type X distribution","volume":"7","author":"Surles","year":"2001","journal-title":"Life Data Anal."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/12\/1096\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:34:08Z","timestamp":1760132048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/12\/1096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,29]]},"references-count":26,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["axioms12121096"],"URL":"https:\/\/doi.org\/10.3390\/axioms12121096","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,29]]}}}