{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T18:32:14Z","timestamp":1775932334836,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,4]],"date-time":"2020-12-04T00:00:00Z","timestamp":1607040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Phase Four of the Brain Korea 21 Project","award":["2020"],"award-info":[{"award-number":["2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.<\/jats:p>","DOI":"10.3390\/sym12122005","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T20:18:22Z","timestamp":1607631502000},"page":"2005","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data"],"prefix":"10.3390","volume":"12","author":[{"given":"Youngseuk","family":"Cho","sequence":"first","affiliation":[{"name":"Department of Statistics, Pusan National University, Busan 46241, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Gyeongsangbuk-do 38453, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/j.2517-6161.1959.tb00349.x","article-title":"The analysis of exponentially distributed lifetimes with two types of failure","volume":"21","author":"Cox","year":"1959","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref_2","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_3","first-page":"237","article-title":"Step stress partially accelerated life testing plan for competing risk using adaptive Type I progressive hybrid censoring","volume":"33","author":"Lone","year":"2017","journal-title":"Pak. J. Stat."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s00180-018-0847-2","article-title":"Bayesian analysis of Weibull distribution based on progressive Type II censored competing risks data with binomial removals","volume":"34","author":"Chacko","year":"2019","journal-title":"Comput. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Nie, J., and Gui, W. (2019). Parameter estimation of Lindley distribution based on progressive Type II censored competing risks data with binomial removals. Mathematics, 7.","DOI":"10.3390\/math7070646"},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"4756","DOI":"10.1080\/03610926.2015.1083111","article-title":"Inference for Weibull distribution under adaptive Type I progressive hybrid censored competing risks data","volume":"46","author":"Ashour","year":"2017","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.cam.2016.11.012","article-title":"Estimation of the inverse Weibull parameters under adaptive Type II progressive hybrid censoring scheme","volume":"315","author":"Nassar","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1016\/j.apm.2015.06.022","article-title":"Estimation for the exponentiated Weibull model with adaptive Type II progressive censored schemes","volume":"40","author":"Sobhi","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Xu, B., and Gui, W. (2019). Entropy estimation of inverse Weibull distribution under adaptive Type II progressive hybrid censoring schemes. Symmetry, 11.","DOI":"10.3390\/sym11121463"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"54691","DOI":"10.1109\/ACCESS.2020.2981497","article-title":"Statistical analysis based on adaptive progressive hybrid censored sample from alpha power generalized exponential distribution","volume":"8","author":"Yan","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lee, H., and Lee, K. (2020). Exact likelihood inference for an exponential parameter under generalized adaptive progressive hybrid censoring. J. Appl. Stat., 12.","DOI":"10.3390\/sym12071149"},{"key":"ref_13","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_14","unstructured":"Lawless, J. (2011). Statistical Models and Methods for Lifetime Data, Wiley."},{"key":"ref_15","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. 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