{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:29:17Z","timestamp":1765960157666,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002608","name":"Daegu University","doi-asserted-by":"publisher","award":["Daegu University Research Grant, 2019"],"award-info":[{"award-number":["Daegu University Research Grant, 2019"]}],"id":[{"id":"10.13039\/501100002608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In many situations of survival and reliability test, the withdrawal of units from the test is pre-planned in order to to free up testing facilities for other tests, or to save cost and time. It is known that several risk factors (RiFs) compete for the immediate failure cause of items. In this paper, we derive an inference for a competing risks model (CompRiM) with a generalized type II progressive hybrid censoring scheme (GeTy2PrHCS). We derive the conditional moment generating functions (CondMgfs), distributions and confidence interval (ConfI) of the scale parameters of exponential distribution (ExDist) under GeTy2PrHCS with CompRiM. A real data set is analysed to illustrate the validity of the method developed here. From the data, it can be seen that the conditional PDFs of MLEs is almost symmetrical.<\/jats:p>","DOI":"10.3390\/sym13050887","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T12:19:57Z","timestamp":1621253997000},"page":"887","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Exact Likelihood Inference for a Competing Risks Model with Generalized Type II Progressive Hybrid Censored Exponential Data"],"prefix":"10.3390","volume":"13","author":[{"given":"Subin","family":"Cho","sequence":"first","affiliation":[{"name":"Department of Statistics, Daegu University, Gyeongsan 38453, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0754-5172","authenticated-orcid":false,"given":"Kyeongjun","family":"Lee","sequence":"additional","affiliation":[{"name":"Division of Mathematics and Big Data Science, Daegu University, Gyeongsan 38453, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alshenawy, R., Al-Alwan, A., Almetwally, E.M., Afify, A.Z., and Almongy, H.M. (2020). Progressive type-II censoring schemes of extended odd Weibull exponential distribution with applications in medicine and engineering. Mathematics, 8.","DOI":"10.3390\/math8101679"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1002\/qre.2610","article-title":"Reliability estimation of a multicomponent stress-strength model for unit Gompertz distribution under progressive Type II censoring","volume":"36","author":"Jha","year":"2020","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chen, S., and Gui, W. (2020). Statistical analysis of a lifetime distribution with a bathtub-shaped failure rate function under adaptive progressive type-II censoring. Mathematics, 8.","DOI":"10.3390\/math8050670"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s42952-019-00022-y","article-title":"Kernel density estimation based on progressive type-II censoring","volume":"49","author":"Helu","year":"2020","journal-title":"J. Korean Stat. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lee, H., and Lee, K. (2020). Exact likelihood inference for an exponential parameter under generalized adaptive progressive hybrid censoring. Symmetry, 12.","DOI":"10.3390\/sym12071149"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jkss.2015.08.003","article-title":"Exact likelihood inference of the exponential parameter under generalized Type II progressive hybrid censoring","volume":"45","author":"Lee","year":"2016","journal-title":"J. Korean Stat. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mahto, A.K., Lodhi, C., Tripathi, Y.M., and Wang, L. (2021). Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive hybrid censoring. J. Appl. Stat., 1\u201329.","DOI":"10.1080\/02664763.2021.1889999"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2492","DOI":"10.1080\/02664763.2020.1815670","article-title":"Inference of progressively type-II censored competing risks data from Chen distribution with an application","volume":"47","author":"Ahmed","year":"2020","journal-title":"J. Appl. Stat."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1080\/03610918.2018.1510522","article-title":"Statistical inference for competing risks model under progressive interval censored Weibull data","volume":"49","author":"Azizi","year":"2020","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Liu, S., and Gui, W. (2020). Estimating the Parameters of the Two-Parameter Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Data with Competing Risks. Mathematics, 8.","DOI":"10.3390\/math8101783"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cho, Y., and Lee, K. (2020). Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data. Symmetry, 12.","DOI":"10.3390\/sym12122005"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0167-7152(02)00267-5","article-title":"An efficient computational method for moments of order statistics under progressive censoring","volume":"60","author":"Balakrishnan","year":"2002","journal-title":"Stat. Probab. Lett."},{"key":"ref_13","unstructured":"Johnson, N.L., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions, Wiley."},{"key":"ref_14","unstructured":"Lawless, J. (2011). Statistical Models and Methods for Lifetime Data, Wiley."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2506","DOI":"10.1080\/00949655.2013.851681","article-title":"Exact inference for competing risks model with generalized type I hybrid censored exponential data","volume":"84","author":"Mao","year":"2014","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"565","DOI":"10.37727\/jkdas.2017.19.2.565","article-title":"Exact inference for competing risks model with generalized progressive hybrid censored exponential data","volume":"19","author":"Cho","year":"2017","journal-title":"J. Korean Data Anal. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/887\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:02:45Z","timestamp":1760162565000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/887"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,17]]},"references-count":16,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["sym13050887"],"URL":"https:\/\/doi.org\/10.3390\/sym13050887","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,5,17]]}}}