{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T07:37:12Z","timestamp":1776411432554,"version":"3.51.2"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T00:00:00Z","timestamp":1587427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Data Anal Classif"],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s11634-020-00391-x","type":"journal-article","created":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T16:10:47Z","timestamp":1587485447000},"page":"355-378","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Mixture modeling of data with multiple partial right-censoring levels"],"prefix":"10.1007","volume":"14","author":[{"given":"Semhar","family":"Michael","sequence":"first","affiliation":[]},{"given":"Tatjana","family":"Miljkovic","sequence":"additional","affiliation":[]},{"given":"Volodymyr","family":"Melnykov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,4,21]]},"reference":[{"key":"391_CR1","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.insmatheco.2014.08.008","volume":"61","author":"SA\u00a0A Bakar","year":"2015","unstructured":"Bakar SA\u00a0A, Hamzaha N\u00a0A, Maghsoudia M, Nadarajah S (2015) Modeling loss data using composite models. Insur Math Econ 61:146\u2013154","journal-title":"Insur Math Econ"},{"key":"391_CR2","doi-asserted-by":"publisher","first-page":"3536","DOI":"10.1016\/j.jspi.2011.05.007","volume":"141","author":"N Balakrishnan","year":"2011","unstructured":"Balakrishnan N, Mitra D (2011) Likelihood inference for lognormal data with left truncation and right censoring with an illustration. J Stat Plan Inference 141:3536\u20133553","journal-title":"J Stat Plan Inference"},{"key":"391_CR3","doi-asserted-by":"publisher","first-page":"4011","DOI":"10.1016\/j.csda.2012.05.004","volume":"56","author":"N Balakrishnan","year":"2012","unstructured":"Balakrishnan N, Mitra D (2012) Left truncated and right censored Weibull data and likelihood inference with an illustration. Comput Stat Data Anal 56:4011\u20134025","journal-title":"Comput Stat Data Anal"},{"key":"391_CR4","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1109\/TR.2013.2273039","volume":"62","author":"N Balakrishnan","year":"2013","unstructured":"Balakrishnan N, Mitra D (2013) Likelihood inference based on left truncated and right censored data from a gamma distribution. IEEE Trans Reliab 62:679\u2013688","journal-title":"IEEE Trans Reliab"},{"key":"391_CR5","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s11222-014-9482-0","volume":"26","author":"S Bang","year":"2016","unstructured":"Bang S, Cho H, Jhun M (2016) Simultaneous estimation for non-crossing multiple quantile regression with right censored data. Statistics and Computing 26:131\u2013147","journal-title":"Statistics and Computing"},{"key":"391_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/0470012382","volume-title":"Statistics of Extremes","author":"J Beirlant","year":"2004","unstructured":"Beirlant J, Goegebeur Y, Teugels J, Segers J (2004) Statistics of Extremes, 1st edn. Wiley, Hobuken, NJ","edition":"1"},{"key":"391_CR7","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/S0167-9473(02)00163-9","volume":"413","author":"C Biernacki","year":"2003","unstructured":"Biernacki C, Celeux G, Govaert G (2003) Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Comput Stat Data Anal 413:561\u2013575","journal-title":"Comput Stat Data Anal"},{"key":"391_CR8","unstructured":"Blostein M, Miljkovic T (2019a) ltmix: Left-Truncated Mixtures of Gamma. Weibull, and Lognormal Distributions, r package version (2)"},{"key":"391_CR9","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.insmatheco.2018.12.001","volume":"85","author":"M Blostein","year":"2019","unstructured":"Blostein M, Miljkovic T (2019) On modeling left-truncated loss data using mixtures of distributions. Insur Math Econ 85:35\u201346","journal-title":"Insur Math Econ"},{"key":"391_CR10","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1007\/s00180-016-0661-7","volume":"31","author":"L Bordes","year":"2016","unstructured":"Bordes L, Chauveau D (2016) Stochastic EM algorithms for parametric and semiparametric mixture models for right-censored lifetime data. Comput Stat 31:1513\u20131538","journal-title":"Comput Stat"},{"key":"391_CR11","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1080\/03461238.2015.1034763","volume":"9","author":"E Calder\u00edn-Ojeda","year":"2016","unstructured":"Calder\u00edn-Ojeda E, Kwok CF (2016) Modeling claims data with composite stoppa models. Scandinavian Actuarial Journal 9:817\u2013836","journal-title":"Scandinavian Actuarial Journal"},{"key":"391_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0378-3758(94)00097-F","volume":"46","author":"D Chauveau","year":"1995","unstructured":"Chauveau D (1995) \u2018A stochastic EM algorithm for mixture with censored data. J Stat Plan 46:1\u201325","journal-title":"J Stat Plan"},{"key":"391_CR13","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1080\/03461230510009763","volume":"5","author":"K Coorey","year":"2005","unstructured":"Coorey K, Ananda MM (2005) Modeling actuarial data with a composite Lognormal-Pareto model. Scandinavian Actuarial Journal 5:321\u2013334","journal-title":"Scandinavian Actuarial Journal"},{"key":"391_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/10920277.1998.10595667","volume":"2","author":"E Frees","year":"1998","unstructured":"Frees E, Valdez E (1998) Understanding relationships using copulas. N Am Actuar J 2:1\u201315","journal-title":"N Am Actuar J"},{"key":"391_CR15","unstructured":"Gruen B, Leisch F, Sarkar D, Mortier F (2019) ltmix: Left-Truncated Mixtures of Gamma, Weibull, and Lognormal Distributions, r package version 2.3-15"},{"key":"391_CR16","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.cam.2018.04.032","volume":"343","author":"W Gui","year":"2018","unstructured":"Gui W, Huang R, Lin XS (2018) Fitting the Erlang mixture model to data via a GEM-CMM algorithm. J Comput Appl Math 343:189\u2013205","journal-title":"J Comput Appl Math"},{"key":"391_CR17","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1214\/ss\/1009212519","volume":"14","author":"JA Hoeting","year":"1999","unstructured":"Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial. Stat Sci 14:382\u2013401","journal-title":"Stat Sci"},{"key":"391_CR18","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert L, Arabie P (1985) Comparing partitions. J Classif 2:193\u2013218","journal-title":"J Classif"},{"key":"391_CR19","volume-title":"Loss Models: From Data to Decisions","author":"S\u00a0A Klugman","year":"2012","unstructured":"Klugman S\u00a0A, Panjer H\u00a0H, Willmot G\u00a0E (2012) Loss Models: From Data to Decisions, 4th edn. Wiley, Hobuken, NJ","edition":"4"},{"key":"391_CR20","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0167-6687(98)00039-0","volume":"24","author":"S\u00a0A Klugman","year":"1999","unstructured":"Klugman S\u00a0A, Parsa R (1999) Fitting bivariate loss distribution with copulas. Insur Math Econ 24:139\u2013148","journal-title":"Insur Math Econ"},{"key":"391_CR21","doi-asserted-by":"publisher","first-page":"2816","DOI":"10.1016\/j.csda.2012.03.003","volume":"56","author":"G Lee","year":"2012","unstructured":"Lee G, Scott C (2012) EM algorithms for multivariate Gaussian mixture models with truncated and censored data. Comput Stat Data Anal 56:2816\u20132829","journal-title":"Comput Stat Data Anal"},{"key":"391_CR22","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1080\/10920277.2010.10597580","volume":"14","author":"SCK Lee","year":"2010","unstructured":"Lee SCK, Lin XS (2010) Modeling and evaluating insurance losses via mixtures of Erlang distributions. N Am Actuar J 14:107\u2013130","journal-title":"N Am Actuar J"},{"key":"391_CR23","doi-asserted-by":"publisher","first-page":"571","DOI":"10.2307\/2531869","volume":"22","author":"G McLachlan","year":"1988","unstructured":"McLachlan G, Jones SAA (1988) Fitting mixture models to grouped and truncated data via the EM algorithm. Biometrics 22:571\u2013578","journal-title":"Biometrics"},{"key":"391_CR24","doi-asserted-by":"publisher","DOI":"10.1002\/0471721182","volume-title":"Finite mixture models","author":"G McLachlan","year":"2000","unstructured":"McLachlan G, Peel D (2000) Finite mixture models. Wiley, Hobuken, NJ"},{"key":"391_CR25","doi-asserted-by":"publisher","first-page":"117","DOI":"10.2143\/AST.27.1.563210","volume":"27","author":"A McNeil","year":"1997","unstructured":"McNeil A (1997) Estimating the tails of loss severity distributions using extreme value theory. ASTIN Bull 27:117\u2013137","journal-title":"ASTIN Bull"},{"key":"391_CR26","first-page":"1","volume-title":"Partitional clustering algorithms","author":"V Melnykov","year":"2015","unstructured":"Melnykov V, Michael S, Melnykov I (2015) Recent developments in model-based clustering with applications. In: Celebi ME (ed) Partitional clustering algorithms. Springer, Berlin, pp 1\u201339"},{"key":"391_CR27","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s11634-016-0264-8","volume":"10","author":"S Michael","year":"2016","unstructured":"Michael S, Melnykov V (2016) An effective strategy for initializing the EM algorithm in finite mixture models. Adv Data Anal Classif 10:563\u2013583","journal-title":"Adv Data Anal Classif"},{"key":"391_CR28","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/j.insmatheco.2016.06.019","volume":"70","author":"T Miljkovic","year":"2016","unstructured":"Miljkovic T, Gr\u00fcn B (2016) Modeling loss data using mixtures of distributions. Insur Math Econ 70:387\u2013396","journal-title":"Insur Math Econ"},{"key":"391_CR29","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1080\/03461231003690754","volume":"3","author":"M Pigeon","year":"2011","unstructured":"Pigeon M, Denuit M (2011) Composite Lognormal\u2013Pareto Model with random threshold. Scandinavian Actuarial Journal 3:177\u2013192","journal-title":"Scandinavian Actuarial Journal"},{"key":"391_CR30","unstructured":"R Core Team (2016) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria"},{"key":"391_CR31","doi-asserted-by":"publisher","first-page":"139","DOI":"10.2143\/AST.27.1.563211","volume":"27","author":"SI Resnick","year":"1997","unstructured":"Resnick SI (1997) Discussion of the Danish data on large fire insurance losses. ASTIN Bull 27:139\u2013151","journal-title":"ASTIN Bull"},{"key":"391_CR32","volume-title":"Introduction to probability models","author":"S\u00a0M Ross","year":"2014","unstructured":"Ross S\u00a0M (2014) Introduction to probability models, 11th edn. Academic Press, New York","edition":"11"},{"key":"391_CR33","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461\u2013464","journal-title":"Ann Stat"},{"key":"391_CR34","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1080\/03461230601110447","volume":"1","author":"DP Scollnik","year":"2007","unstructured":"Scollnik DP (2007) On composite Lognormal-Pareto models. Scan Actuar J 1:20\u201333","journal-title":"Scan Actuar J"},{"key":"391_CR35","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.csda.2017.09.005","volume":"118","author":"Z Sun","year":"2018","unstructured":"Sun Z, Ye X, Sun L (2018) Consistent test for parametric models with right-censored data using projections. Comput Stat Data Anal 118:112\u2013125","journal-title":"Comput Stat Data Anal"},{"key":"391_CR36","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1017\/asb.2015.15","volume":"45","author":"R Verbelen","year":"2015","unstructured":"Verbelen R, Gong L, Antonio K, Badescu A, Lin S (2015) Fitting mixtures of Erlangs to censored and truncated data using the EM algorithm. ASTIN Bull 45:729\u2013758","journal-title":"ASTIN Bull"}],"container-title":["Advances in Data Analysis and Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-020-00391-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11634-020-00391-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-020-00391-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T01:12:37Z","timestamp":1618967557000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11634-020-00391-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,21]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["391"],"URL":"https:\/\/doi.org\/10.1007\/s11634-020-00391-x","relation":{},"ISSN":["1862-5347","1862-5355"],"issn-type":[{"value":"1862-5347","type":"print"},{"value":"1862-5355","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,21]]},"assertion":[{"value":"22 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 March 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}