{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T11:00:58Z","timestamp":1780657258054,"version":"3.54.1"},"reference-count":34,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T00:00:00Z","timestamp":1560643200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009157","name":"Jomo Kenyatta University of Agriculture and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100009157","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2019,6,16]]},"abstract":"<jats:p>In this article, we are interested in developing an alternative estimation method of the parameters of the hybrid log-Poisson regression model. In our previous paper, we have proposed a hybrid log-Poisson regression model where we have derived the analytical expression of the fuzzy parameters. We found that the hybrid model provide better results than the classical log-Poisson regression model according to the mean square error prediction and the goodness of fit index. However, nowhere we have taken into account the optimal value of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>\u03b1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>cut) which is of greatest importance in fuzzy regressions literature. In this paper, we provide an alternative estimation method of our hybrid model using a quadratic optimization program and the optimized <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>h<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>value (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>\u03b1<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>cut). The expected value of fuzzy number is used as a defuzzification procedure to move from fuzzy values to crisp values. We perform the hybrid model with the alternative estimation we are suggesting on two different numerical data to predict incremental payments in loss reserving. From the mean square error prediction, we prove that the alternative estimation of the new hybrid model with an optimized <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>h<\/mml:mi><mml:mo>-<\/mml:mo><\/mml:math>value predicts incremental payments better than the classical log-Poisson regression model as well as the same hybrid model with analytical estimation of parameters. Hence we have optimized the outstanding loss reserves.<\/jats:p>","DOI":"10.1155\/2019\/1393946","type":"journal-article","created":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T19:30:32Z","timestamp":1560713432000},"page":"1-14","source":"Crossref","is-referenced-by-count":3,"title":["An Estimation of a Hybrid Log-Poisson Regression Using a Quadratic Optimization Program for Optimal Loss Reserving in Insurance"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1660-1033","authenticated-orcid":true,"given":"Apollinaire","family":"Woundjiagu\u00e9","sequence":"first","affiliation":[{"name":"Institute of Basic Sciences Technology and Innovation, Pan African University-Jomo Kenyatta University of Agriculture and Technology, P.O. Box 62000-00200, Nairobi, Kenya"},{"name":"National Advanced School of Engineering, University of Maroua, P.O. Box 46 Maroua, Cameroon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9345-7381","authenticated-orcid":true,"given":"Martin Le Doux","family":"Mbele Bidima","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronald","family":"Waweru Mwangi","sequence":"additional","affiliation":[{"name":"School of Computing and Information Technology, Jomo Kenyatta University of Agriculture and Technology, P.O. Box 62000-00200, Nairobi, Kenya"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"46","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-018-0564-6"},{"issue":"112","key":"2","first-page":"181","volume":"59","year":"1972","journal-title":"In Proceedings of the Casualty Actuarial Society"},{"key":"3","volume":"1","year":"1986"},{"key":"4","year":"1981"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.2660062"},{"key":"6","volume":"435","year":"2008"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2143\/AST.21.1.2005403"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/S1357321700003809"},{"key":"35","year":"1981"},{"key":"36","first-page":"D5.1","volume":"2","year":"2014","journal-title":"Claims Reserving Manual"},{"key":"37","first-page":"1038","volume-title":"Report lag distributions: estimation and application to IBNR counts","year":"1988"},{"key":"38","first-page":"112","volume-title":"Chain ladder reserving methods for liabilities with per occurrence limits","year":"2013"},{"issue":"2","key":"39","first-page":"138","volume":"8","year":"2014","journal-title":"Variance: Advancing the Science of Risk"},{"issue":"2","key":"41","first-page":"845","volume":"40","year":"2010","journal-title":"The Journal of the International Actuarial Association"},{"issue":"55","key":"42","first-page":"101","volume":"1","year":"1998","journal-title":"In CAS Forum Fall"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.2143\/AST.36.2.2017933"},{"key":"44","volume-title":"The estimation of loss development tail factors: a summary report","year":"2013"},{"issue":"1","key":"45","first-page":"1","volume":"42","year":"2012","journal-title":"The Journal of the International Actuarial Association"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03364-7"},{"issue":"3","key":"22","first-page":"338","volume":"8","year":"1965","journal-title":"Information and Computation"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1080\/00207727808941724"},{"key":"16","first-page":"112","year":"1993","journal-title":"In Readings in Fuzzy Sets for Intelligent Systems"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48753-8"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2006.03.004"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90046-8"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90017-1"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1967.264750"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00370-4"},{"key":"29","year":"1991"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2015.02.011"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1017\/S1357321700000222"},{"key":"33","year":"2006"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.03.033"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2019\/1393946.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2019\/1393946.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2019\/1393946.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T19:30:37Z","timestamp":1560713437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2019\/1393946\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,16]]},"references-count":34,"alternative-id":["1393946","1393946"],"URL":"https:\/\/doi.org\/10.1155\/2019\/1393946","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"value":"1687-7101","type":"print"},{"value":"1687-711X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,16]]}}}