{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T05:31:19Z","timestamp":1769837479415,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s40314-022-01875-6","type":"journal-article","created":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T14:12:12Z","timestamp":1652278332000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A novel claim size distribution based on a Birnbaum\u2013Saunders and gamma mixture capturing extreme values in insurance: estimation, regression, and applications"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-7908","authenticated-orcid":false,"given":"Emilio","family":"G\u00f3mez\u2013D\u00e9niz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-3270","authenticated-orcid":false,"given":"V\u00edctor","family":"Leiva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6364-627X","authenticated-orcid":false,"given":"Enrique","family":"Calder\u00edn\u2013Ojeda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1522-9292","authenticated-orcid":false,"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,5,11]]},"reference":[{"key":"1875_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119412540","volume-title":"Reinsurance: actuarial and statistical aspects","author":"H Albrecher","year":"2017","unstructured":"Albrecher H, Beirlant J, Eugels J (2017) Reinsurance: actuarial and statistical aspects. Wiley, New York"},{"key":"1875_CR2","volume-title":"Pareto distributions","author":"B Arnold","year":"1983","unstructured":"Arnold B (1983) Pareto distributions. International Cooperative Publishing House, Silver Spring"},{"key":"1875_CR3","doi-asserted-by":"publisher","first-page":"21","DOI":"10.3390\/risks6010021","volume":"6","author":"RG Aykroyd","year":"2018","unstructured":"Aykroyd RG, Leiva V, Marchant C (2018) Multivariate Birnbaum\u2013Saunders distributions: modelling and applications. Risks 6:21","journal-title":"Risks"},{"key":"1875_CR4","doi-asserted-by":"publisher","first-page":"3887","DOI":"10.1016\/j.csda.2012.05.007","volume":"56","author":"C Azevedo","year":"2012","unstructured":"Azevedo C, Leiva V, Athayde E, Balakrishnan N (2012) Shape and change point analyses of the Birnbaum\u2013Saunders-t hazard rate and associated estimation. Comput Stat Data Anal 56:3887\u20133897","journal-title":"Comput Stat Data Anal"},{"key":"1875_CR5","volume-title":"Practical analysis of extreme values","author":"J Beirlant","year":"1996","unstructured":"Beirlant J, Teugels J, Vynckier P (1996) Practical analysis of extreme values. Leuven University Press, Leuve"},{"key":"1875_CR6","first-page":"41","volume":"31","author":"J Beirlant","year":"2005","unstructured":"Beirlant J, Matthys GJ, Dierckx G (2005) Heavy-tailed distributions and rating. Astin Bull 31:41\u201362","journal-title":"Astin Bull"},{"key":"1875_CR7","doi-asserted-by":"publisher","first-page":"319","DOI":"10.2307\/3212003","volume":"6","author":"ZW Birnbaum","year":"1969","unstructured":"Birnbaum ZW, Saunders SC (1969) A new family of life distributions. J Appl Probab 6:319\u2013327","journal-title":"J Appl Probab"},{"key":"1875_CR8","doi-asserted-by":"publisher","DOI":"10.1201\/9781584886969","volume-title":"Statistical and probabilistic methods in actuarial science","author":"P Boland","year":"2007","unstructured":"Boland P (2007) Statistical and probabilistic methods in actuarial science. Chapman and Hall, New York"},{"key":"1875_CR9","volume-title":"RATS handbook to accompany introductory econometrics for finance","author":"C Brooks","year":"2009","unstructured":"Brooks C (2009) RATS handbook to accompany introductory econometrics for finance. Cambridge University Press, Cambridge"},{"key":"1875_CR10","volume-title":"A course in credibility theory and its applications","author":"H B\u00fchlmann","year":"2005","unstructured":"B\u00fchlmann H, Gisler A (2005) A course in credibility theory and its applications. Springer, New York"},{"key":"1875_CR11","doi-asserted-by":"publisher","first-page":"60","DOI":"10.3390\/risks5040060","volume":"5","author":"E Calder\u00edn-Ojeda","year":"2017","unstructured":"Calder\u00edn-Ojeda E, Fergusson K, Wu X (2017) An EM algorithm for double-Pareto-lognormal generalized linear model applied to heavy-tailed insurance claims. Risks 5:60","journal-title":"Risks"},{"key":"1875_CR12","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s00477-020-01767-3","volume":"34","author":"JMF Carrasco","year":"2020","unstructured":"Carrasco JMF, Figueroa-Zuniga J, Leiva V, Riquelme M, Aykroyd RG (2020) An errors-in-variables model based on the Birnbaum\u2013Saunders and its diagnostics with an application to earthquake data. Stoch Environ Res Risk Assess 34:369\u2013380","journal-title":"Stoch Environ Res Risk Assess"},{"key":"1875_CR13","doi-asserted-by":"publisher","first-page":"2861","DOI":"10.1080\/00949655.2020.1790560","volume":"90","author":"M Desousa","year":"2020","unstructured":"Desousa M, Saulo H, Leiva V, Santos-Neto M (2020) On a new mixture-based regression model: simulation and application to data with high censoring. J Stat Comput Simul 90:2861\u20132877","journal-title":"J Stat Comput Simul"},{"key":"1875_CR14","doi-asserted-by":"crossref","unstructured":"Efron B, Tibshirani R (1993) An introduction to the bootstrap. Chapman and Hall, New York","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"1875_CR15","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1080\/10920277.1999.10595797","volume":"3","author":"P Embrechts","year":"1999","unstructured":"Embrechts P, Resnick S, Samorodnitsky G (1999) Extreme value theory as a risk management tool. N Am Actuarial J 3:30\u201341","journal-title":"N Am Actuarial J"},{"key":"1875_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-021-01260-1","author":"J Figueroa-Zuniga","year":"2022","unstructured":"Figueroa-Zuniga J, Bayes CL, Leiva V, Liu S (2022) Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications. Stat Pap. https:\/\/doi.org\/10.1007\/s00362-021-01260-1 (in press)","journal-title":"Stat Pap"},{"key":"1875_CR17","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.chemolab.2018.03.012","volume":"177","author":"F Garcia-Papani","year":"2018","unstructured":"Garcia-Papani F, Leiva V, Uribe-Opazo MA, Aykroyd RG (2018) Birnbaum\u2013Saunders spatial regression models: diagnostics and application to chemical data. Chemom Intell Lab Syst 177:114\u2013128","journal-title":"Chemom Intell Lab Syst"},{"key":"1875_CR18","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1016\/j.insmatheco.2007.09.002","volume":"42","author":"E G\u00f3mez-D\u00e9niz","year":"2008","unstructured":"G\u00f3mez-D\u00e9niz E (2008) A generalization of the credibility theory obtained by using the weighted balanced loss function. Insur Math Econ 42:850\u2013854","journal-title":"Insur Math Econ"},{"issue":"4","key":"1875_CR19","doi-asserted-by":"publisher","first-page":"585","DOI":"10.4310\/SII.2019.v12.n4.a8","volume":"12","author":"F Hashemi","year":"2019","unstructured":"Hashemi F, Naderi M, Jamalizadeh A (2019) Normal mean-variance Lindley Birnbaum-Saunders distribution. Stat Interface 12(4):585\u2013597","journal-title":"Stat Interface"},{"key":"1875_CR20","doi-asserted-by":"crossref","unstructured":"Hashemi F, Naderi M, Mashinchi M (2019) Clustering right-skewed data stream via Birnbaum-Saunders mixture models: a flexible approach based on fuzzy clustering algorithm. Appl Soft Comput 82:105539","DOI":"10.1016\/j.asoc.2019.105539"},{"key":"1875_CR21","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.chemolab.2019.04.013","volume":"190","author":"M Huerta","year":"2019","unstructured":"Huerta M, Leiva V, Liu S, Rodriguez M, Villegas D (2019) On a partial least squares regression model for asymmetric data with a chemical application in mining. Chemom Intell Lab Syst 190:55\u201368","journal-title":"Chemom Intell Lab Syst"},{"key":"1875_CR22","doi-asserted-by":"crossref","unstructured":"Jessen AH, Mikosch T (2006) Regularly varying functions. Publ Inst Mat 80:171\u2013192","DOI":"10.2298\/PIM0694171J"},{"key":"1875_CR23","doi-asserted-by":"crossref","unstructured":"Konstantinides D (2018) Risk theory. A heavy tail approach. World Scientific Publishing, New York","DOI":"10.1142\/10523"},{"key":"1875_CR24","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s40314-021-01418-5","volume":"40","author":"M\u00c7 Korkmaz","year":"2021","unstructured":"Korkmaz M\u00c7, Chesneau C (2021) On the unit Burr-XII distribution with the quantile regression modeling and applications. Comput Appl Math 40:29","journal-title":"Comput Appl Math"},{"key":"1875_CR25","doi-asserted-by":"crossref","unstructured":"Leiva V (2016) The Birnbaum\u2013Saunders distribution. Academic Press, New York","DOI":"10.1016\/B978-0-12-803769-0.00003-0"},{"key":"1875_CR26","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1002\/for.2718","volume":"40","author":"V Leiva","year":"2021","unstructured":"Leiva V, Saulo H, Souza R, Aykroyd RG, Vila R (2021) A new BISARMA time series model for forecasting mortality using weather and particulate matter data. J Forecast 40:346\u2013364","journal-title":"J Forecast"},{"key":"1875_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2021.104849","volume":"188","author":"S Liu","year":"2021","unstructured":"Liu S, Leiva V, Zhuang D, Ma T, Figueroa-Zuniga J (2021) Matrix differential calculus with applications in the multivariate linear model and its diagnostics. J Multivar Anal 188:104849","journal-title":"J Multivar Anal"},{"key":"1875_CR28","doi-asserted-by":"crossref","unstructured":"Marchant C, Leiva V, Cysneiros FJA (2016) A multivariate log-linear model for Birnbaum\u2013Saunders distributions. IEEE Trans Reliab 65:816\u2013827","DOI":"10.1109\/TR.2015.2499964"},{"key":"1875_CR29","doi-asserted-by":"crossref","unstructured":"Martinez S, Giraldo R, Leiva V (2019) Birnbaum\u2013Saunders functional regression models for spatial data. Stoch Environ Res Risk Assess 33:1765\u20131780","DOI":"10.1007\/s00477-019-01708-9"},{"key":"1875_CR30","doi-asserted-by":"crossref","unstructured":"Naderi M, Hashemi F, Bekker A, Jamalizadeh A (2020) Modeling right-skewed financial data streams: a likelihood inference based on the generalized Birnbaum\u2013Saunders mixture model. Appl Math Comput 376:125109","DOI":"10.1016\/j.amc.2020.125109"},{"key":"1875_CR31","doi-asserted-by":"crossref","unstructured":"Naderi M, Mozafari M, Okhli K (2020) Finite mixture modeling via skew-Laplace Birnbaum\u2013Saunders distribution. J Stat Theory Appl 19:49\u201358","DOI":"10.2991\/jsta.d.200224.008"},{"issue":"255","key":"1875_CR32","first-page":"1","volume":"40","author":"TF Ribeiro","year":"2021","unstructured":"Ribeiro TF, Cordeiro GM, Pe\u00f1a-Ram\u00edrez FA, Guerra RR (2021) A new quantile regression for the COVID-19 mortality rates in the United States. Comput Appl Math 40(255):1\u201316","journal-title":"Comput Appl Math"},{"key":"1875_CR33","doi-asserted-by":"crossref","unstructured":"Rolski T, Schmidli H, Schmidt V, Teugel J (1999) Stochastic processes for insurance and finance. Wiley, New York","DOI":"10.1002\/9780470317044"},{"key":"1875_CR34","unstructured":"Ruskeepaa H (2009) Mathematica navigator. Mathematics, statistics, and graphics. Academic Press, New York"},{"key":"1875_CR35","doi-asserted-by":"publisher","first-page":"1000","DOI":"10.3390\/math8061000","volume":"8","author":"L Sanchez","year":"2020","unstructured":"Sanchez L, Leiva V, Galea M, Saulo H (2020) Birnbaum-Saunders quantile regression models with application to spatial data. Mathematics 8:1000","journal-title":"Mathematics"},{"key":"1875_CR36","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1002\/asmb.2556","volume":"37","author":"L Sanchez","year":"2021","unstructured":"Sanchez L, Leiva V, Galea M, Saulo H (2021) Birnbaum-Saunders quantile regression and its diagnostics with application to economic data. Appl Stoch Model Bus Ind 37:53\u201373","journal-title":"Appl Stoch Model Bus Ind"},{"key":"1875_CR37","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1111\/stan.12243","volume":"76","author":"H Saulo","year":"2022","unstructured":"Saulo H, Dasilva A, Leiva V, Sanchez L, de la Fuente-Mella H (2022) Log-symmetric quantile regression models. Stat Neerl 76:124\u2013163","journal-title":"Stat Neerl"},{"key":"1875_CR38","doi-asserted-by":"crossref","unstructured":"Villegas C, Paula GA, Leiva V (2011) Birnbaum\u2013Saunders mixed models for censored reliability data analysis. IEEE Trans Reliab 60:748\u2013758","DOI":"10.1109\/TR.2011.2170251"},{"key":"1875_CR39","doi-asserted-by":"publisher","first-page":"307","DOI":"10.2307\/1912557","volume":"57","author":"Q Vuong","year":"1989","unstructured":"Vuong Q (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57:307\u2013333","journal-title":"Econometrica"},{"key":"1875_CR40","doi-asserted-by":"crossref","unstructured":"Wilcox R (2010) Fundamentals of modern statistical methods. Substantially improving power and accuracy. Springer, New York","DOI":"10.1007\/978-1-4419-5525-8"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01875-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01875-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01875-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,4]],"date-time":"2023-02-04T22:43:49Z","timestamp":1675550629000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01875-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,11]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1875"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01875-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,11]]},"assertion":[{"value":"3 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"171"}}