{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:17:50Z","timestamp":1760231870039,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T00:00:00Z","timestamp":1665014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SEMILLERO UA-2022 project, Chile"},{"name":"Universidad de C\u00f3rdoba, Monter\u00eda, Colombia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We focus on a variety of bivariate models with proportional hazard components. Models with proportional hazard marginals are described together with a selection of models with propor- tional hazard conditional distributions. The bivariate distributions with marginal proportional hazards distributions are shown to be closely related to certain known bivariate exponential models. Two distinct kinds of conditional specification are investigated. Discussion is provided of cases with hazard function components that are (1) completely unknown, (2) known to belong to given parametric families and (3) completely known. Since the models are designed for use with survival data, it is inevitable that the marginal and conditional distributions will be asymmetric. However, logarithmic transformations in some cases will result in symmetric component distributions.<\/jats:p>","DOI":"10.3390\/sym14102073","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T03:32:56Z","timestamp":1665459176000},"page":"2073","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bivariate Proportional Hazard Models: Structure and Inference"],"prefix":"10.3390","volume":"14","author":[{"given":"Barry C.","family":"Arnold","sequence":"first","affiliation":[{"name":"Statistics Department, University of California Riverside, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6441-5377","authenticated-orcid":false,"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias, Universidad de C\u00f3rdoba, C\u00f3rdoba 2300, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1080\/01621459.1967.10482885","article-title":"A Multivariate Exponential Distribution","volume":"62","author":"Marshall","year":"1967","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kotz, S., Balakrishnan, N., and Johnson, N.L. (2000). Continuous Multivariate Distributions, John Wiley and Sons.","DOI":"10.1002\/0471722065"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1080\/01621459.1988.10478627","article-title":"Bivariate distributions with exponential conditionals","volume":"83","author":"Arnold","year":"1988","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jewell, N.P., Kimber, A.C., Lee, M.L.T., and Whitmore, G.A. (1996). Conditional proportional hazards models. Lifetime Data: Models in Reliability and Survival Analysis, Springer.","DOI":"10.1007\/978-1-4757-5654-8"},{"key":"ref_5","unstructured":"Arnold, B.C., Castillo, E., and Sarabia, J.M. (1999). Conditional Specification of Statistical Models, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1080\/01621459.1960.10483368","article-title":"Bivariate Exponential Distributions","volume":"55","author":"Gumbel","year":"1960","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_7","first-page":"179","article-title":"Statistical Analysis of Non-Lattice Data","volume":"24","author":"Besag","year":"1975","journal-title":"J. R. Stat. Soc. Ser. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1111\/j.2517-6161.1991.tb01829.x","article-title":"Bivariate distributions with conditionals in prescribed exponential families","volume":"53","author":"Arnold","year":"1991","journal-title":"J. R. Stat. Soc. Ser. 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A bivariate power Lindley survival distribution, Unpublished Work."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1080\/01621459.1967.10482930","article-title":"Some Analytical Properties of Bivariate Extremal Distributions","volume":"62","author":"Gumbel","year":"1967","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Stat."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2073\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:06Z","timestamp":1760143626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2073"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,6]]},"references-count":15,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14102073"],"URL":"https:\/\/doi.org\/10.3390\/sym14102073","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,10,6]]}}}