@string{AB = {ASTIN Bulletin}}
@string{IME = {Insurance: Mathematics and Economics}}
@string{MVSVM = {Bulletin of the Swiss Association of Actuaries}}
@string{NAAJ = {North American Actuarial Journal}}

@Book{Abramowitz:1972,
  author = 	 {Abramowitz, M. and Stegun, I. A.},
  title = 	 {Handbook of Mathematical Functions},
  publisher = 	 {Dover},
  year = 	 1972,
  language = 	 {english}
}

@Book{Arnold:pareto:2ed,
  author = 	 {Arnold,  B. C.},
  title = 	 {{P}areto Distributions},
  publisher = 	 {{CRC} {P}ress},
  year 	= 	 2015,
  edition = 	 2,
  isbn 	= 	 {978-1-46658485-3}
}

@Article{AsmussenRolski_91,
  author = 	 {Asmussen, S. and Rolski, T.},
  title = 	 {Computational methods in risk theory: a
                  matrix-algorithmic approach},
  journal = 	 IME,
  year = 	 1991,
  volume = 	 10,
  pages = 	 {259-274},
  language =	 {english}
}

@Article{BJ_87,
  author =	 {Bühlmann, H. and Jewell, W. S.},
  title =	 {Hierarchical credibility revisited},
  year =	 1987,
  journal =	 MVSVM,
  volume =	 87,
  pages =	 {35-54},
  language =	 {english}
}

@Article{BS_70,
  author =	 {Bühlmann, H. and Straub, E.},
  title =	 {Glaubgwürdigkeit für {S}chadensätze},
  year =	 1970,
  journal =	 MVSVM,
  volume =	 70,
  pages =	 {111-133}
}

@Book{Bateman:1953:2,
  author = 	 {Bateman, H.},
  title = 	 {Higher transcendental functions},
  volume = 	 2,
  publisher = 	 {McGraw-Hill},
  year = 	 1953,
}

@InCollection{BeekmanFormula_EAS,
  author = 	 {Kass, R.},
  title = 	 {Beekman's convolution formula},
  booktitle = 	 {Encyclopedia of actuarial science},
  publisher = 	 {Wiley},
  year = 	 2004,
  editor =	 {J. L. Teugels and B. Sundt},
  volume =	 1,
  ISBN =	 {0-4708467-6-3},
  language =	 {english}
}

@Article{Beekman_68,
  author = 	 {Beekman, J. A.},
  title = 	 {Collective risk results},
  journal = 	 {Transactions of the Society of Actuaries},
  year = 	 1968,
  volume = 	 20,
  pages = 	 {182-199},
  language =	 {english}
}

@Article{Buhlmann:regression:1997,
  author = 	 {Bühlmann, H. and Gisler, A.},
  title = 	 {Credibility in the regression case revisited},
  journal = 	 AB,
  year = 	 1997,
  volume = 	 27,
  pages = 	 {83-98},
  language =	 {english}
}

@Article{Buhlmann_69,
  author =	 {Bühlmann, H.},
  title =	 {Experience rating and credibility},
  year =	 1969,
  journal =	 AB,
  volume =	 5,
  pages =	 {157-165},
  language =	 {english}
}

@Book{Buhlmann_Gisler,
  author =	 {Bühlmann, H. and Gisler, A.},
  title = 	 {A course in credibility theory and its applications},
  publisher = 	 {Springer},
  year = 	 2005,
  isbn =	 {3-5402575-3-5},
  language =	 {english}
}

@Article{Centeno_02,
  author = 	 {Centeno, M. {d.} L.},
  title = 	 {Measuring the effects of reinsurance by the
                  adjustment coefficient in the Sparre-Anderson model},
  journal = 	 IME,
  year = 	 2002,
  volume = 	 30,
  pages = 	 {37-49}
}

@Misc{Dalgaard:r-help:2005,
  author = 	 {Dalgaard, P.},
  title = 	 {simulate zero-truncated {P}oisson distribution},
  howpublished = {\texttt{r-help} mailing list},
  month = 	 {May 1},
  year = 	 2005,
  url = 	 {https://stat.ethz.ch/pipermail/r-help/2005-May/070680.html},
  language = 	 {english}
}

@Book{Daykin_et_al,
  author =	 {Daykin, C.D. and Pentikäinen, T. and Pesonen, M.},
  title =	 {Practical Risk Theory for Actuaries},
  publisher =	 {Chapman \& Hall},
  year =	 1994,
  address =	 {London},
  isbn =	 {0-4124285-0-4},
  language =	 {english}
}

@Book{DenuitCharpentier1,
  author =	 {Denuit, M. and Charpentier, A.},
  title = 	 {Math\'ematiques de l'assurance non-vie},
  publisher = 	 {Economica},
  year = 	 2004,
  volume =	 {1, Principes fondamentaux de th\'eorie du risque},
  address =	 {Paris},
  isbn =	 {2-7178485-4-1},
  language =	 {francais}
}

@Manual{GSL,
  title = 	 {{GNU} Scientific Library Reference Manual},
  author = 	 {Galassi, M. and Davies, J. and Theiler, J. and
                  Gough, B. and Jungman, G. and Alken P. and Booth, M.
                  and Rossi, F. and Ulerich, R.},
  edition = 	 {Third},
  isbn = 	 {0-95461207-8},
  url = 	 {https://www.gnu.org/software/gsl/},
  language = 	 {english}
}

@Book{Gerber_MRT,
  author =	 {Gerber, H. U.},
  title =	 {An Introduction to Mathematical Risk Theory},
  publisher =	 {Huebner Foundation},
  year =	 1979,
  address =	 {Philadelphia},
  language =	 {english}
}

@Article{Goulet:lossdist:2008,
  author = 	 {Goulet, V. and Pigeon, M.},
  title = 	 {Statistical Modeling of Loss Distributions Using
                  \pkg{actuar}},
  journal = 	 {R News},
  year = 	 2008,
  volume = 	 8,
  number = 	 1,
  pages = 	 {34-40},
  month = 	 {May},
  url = 	 {https://journal.r-project.org/articles/RN-2008-006/},
  language =	 {english}
}

@Article{Goulet:simpf:2008,
  author = 	 {Goulet, V. and Pouliot, L.-P.},
  title = 	 {Simulation of Compound Hierarchical Models in {R}},
  journal = 	 NAAJ,
  year = 	 2008,
  volume =	 12,
  pages =	 {401-412},
  language =	 {english}
}

@Article{Goulet_JAP,
  author =	 {Goulet, V.},
  title =	 {Principles and application of credibility theory},
  year =	 1998,
  journal =	 {Journal of Actuarial Practice},
  volume =	 6,
  pages =	 {5-62},
  language =	 {english}
}

@Article{Goulet_cfs,
  author = 	 {Forgues, A. and Goulet, V. and Lu, J.},
  title = 	 {Credibility for severity revisited},
  journal = 	 NAAJ,
  year = 	 2006,
  volume =	 10,
  number =	 1,
  pages = 	 {49-62},
  language =	 {english}
}

@InProceedings{Hachemeister_75,
  author =	 {Hachemeister, C. A.},
  title =	 {Credibility for Regression Models with Application
                  to Trend},
  year =	 1975,
  booktitle =	 {Credibility, theory and applications},
  series =	 {Proceedings of the berkeley Actuarial Research
                  Conference on Credibility},
  pages =	 {129-163},
  publisher =	 {Academic Press},
  address =	 {New York},
  language =	 {english}
}

@Book{HoggKlugman,
  author =	 {Hogg, R. V. and Klugman, S. A.},
  title =	 {Loss Distributions},
  publisher =	 {Wiley},
  year =	 1984,
  address =	 {New York},
  isbn =	 {0-4718792-9-0},
  language =	 {english}
}

@Article{Holla:PIG:1966,
  author = 	 {Holla, M. S.},
  title = 	 {On a {P}oisson-Inverse {G}aussian Distribution},
  journal = 	 {Metrika},
  year = 	 1966,
  volume = 	 15,
  pages = 	 {377-384},
  language =	 {english}
}

@Article{Jewell_75,
  author =	 {Jewell, W. S.},
  title =	 {The use of collateral data in credibility theory: a
                  hierarchical model},
  year =	 1975,
  journal =	 {Giornale dell'Istituto Italiano degli Attuari},
  volume =	 38,
  pages =	 {1-16},
  language =	 {english}
}

@Book{Johnson:discrete:2005,
  author =	 {Johnson, N. L. and Kemp, A. W. and Kotz, S.},
  title =	 {Univariate Discrete Distributions},
  publisher =	 {Wiley},
  year =	 2005,
  edition =	 3,
  isbn =         {978-047127246-5},
  language =	 {english}
}

@Book{LivreVert,
  author =	 {Goovaerts, M. J. and Hoogstad, W. J.},
  title =	 {Credibility theory},
  series =	 {Surveys of actuarial studies},
  number =	 4,
  year =	 1987,
  publisher =	 {Nationale-Nederlanden N.V.},
  address =	 {Netherlands},
  language =	 {english}
}

@Book{LossModels,
  author =	 {Klugman, S. A. and Panjer, H. H. and Willmot, G.},
  title = 	 {Loss Models: From Data to Decisions},
  publisher = 	 {Wiley},
  year = 	 1998,
  address =	 {New York},
  isbn =         {0-4712388-4-8},
  language =	 {english}
}

@Book{LossModels2e,
  author =	 {Klugman, S. A. and Panjer, H. H. and Willmot, G.},
  title = 	 {Loss Models: From Data to Decisions},
  edition =      2,
  publisher = 	 {Wiley},
  year = 	 2004,
  address =	 {New York},
  isbn =         {0-4712157-7-5},
  language =	 {english}
}

@Book{LossModels3e,
  author =	 {Klugman, S. A. and Panjer, H. H. and Willmot, G.},
  title = 	 {Loss Models: From Data to Decisions},
  edition =      3,
  publisher = 	 {Wiley},
  year = 	 2008,
  address =	 {New York},
  isbn =         {978-0-4701878-1-4},
  language =	 {english}
}

@Book{LossModels4e,
  author =	 {Klugman, S. A. and Panjer, H. H. and Willmot, G.},
  title = 	 {Loss Models: From Data to Decisions},
  edition =      4,
  publisher = 	 {Wiley},
  year = 	 2012,
  address =	 {New York},
  isbn =         {978-1-118-31532-3},
  language =	 {english}
}

@Book{MART,
  author =	 {Kaas, R. and Goovaerts, M. and Dhaene, J. and Denuit, M.},
  title = 	 {Modern actuarial risk theory},
  publisher = 	 {Kluwer {A}cademic {P}ublishers},
  year = 	 2001,
  address =	 {Dordrecht},
  isbn =	 {0-7923763-6-6},
  language =	 {english}
}

@Book{MART:2e,
  author =	 {Kaas, R. and Goovaerts, M. and Dhaene, J. and Denuit, M.},
  title = 	 {Modern Actuarial Risk Theory. Using {R}},
  edition =	 2,
  publisher = 	 {Springer},
  year = 	 2008,
  isbn =	 {978-3-54070992-3},
  language =	 {english}
}

@Book{MASS,
  author =	 {Venables, W. N. and Ripley, B. D.},
  title =	 {Modern applied statistics with {S}},
  publisher =	 {Springer},
  year =	 2002,
  edition =	 4,
  address =	 {New York},
  isbn =	 {0-3879545-7-0},
  language =	 {english}
}

@Manual{Matrix,
  title = 	 {Matrix: A Matrix package for R},
  author = 	 {Bates, D. and Maechler, M.},
  year = 	 2016,
  url = 	 {http://cran.r-project.org/package=Matrix},
}

@Book{Neuts_81,
  author = 	 {Neuts, M. F.},
  title = 	 {Matrix-geometric solutions in stochastic models: an
                  algorithmic approach},
  publisher = 	 {Dover Publications},
  year = 	 1981,
  isbn = 	 {978-0-4866834-2-3},
  language =	 {english}
}

@Unpublished{Ohlsson,
  author = 	 {Ohlsson, E.},
  title = 	 {Simplified estimation of structure parameters in
                  hierarchical credibility},
  year = 	 2005,
  note = 	 {Presented at the Zurich ASTIN Colloquium},
  url = 	 {https://www.actuaries.org/ASTIN/Colloquia/Zurich/Ohlsson.pdf},
  language =	 {english}
}

@Article{Panjer_81,
  author = 	 {Panjer, H. H.},
  title = 	 {Recursive evaluation of a family of compound distributions},
  journal = 	 AB,
  year = 	 1981,
  volume = 	 12,
  pages = 	 {22-26},
  language =	 {english}
}

@Manual{R-exts,
  title =	 {Writing {R} Extensions},
  author =	 {{R Core Team}},
  organization = {R Foundation for Statistical Computing},
  address =	 {Vienna, Austria},
  year =	 2020,
  url =		 {https://cran.r-project.org/doc/manuals/R-exts.html},
  language =	 {english}
}

@Article{Scollnik:2001:MCMC,
  author = 	 {Scollnik, D. P. M.},
  title = 	 {Actuarial Modeling with {MCMC} and {BUGS}},
  journal = 	 {North American Actuarial Journal},
  year = 	 2001,
  volume = 	 5,
  number = 	 2,
  pages = 	 {96-124},
  language =	 {english}
}

@Article{Shaban:PIG:1981,
  author = 	 {Shaban, S. A.},
  title = 	 {Computation of the {P}oisson-inverse {G}aussian distribution},
  journal = 	 {Communications in Statistics -- Theory and Methods},
  year = 	 1981,
  volume = 	 10,
  number =  	 14,
  pages = 	 {1389-1399},
  language =	 {english}
}

@Manual{SuppDists,
  title = 	 {SuppDists: Supplementary distributions},
  author = 	 {Wheeler, B.},
  year = 	 2016,
  url = 	 {http://cran.r-project.org/package=SuppDists}
}

@Book{Thomopoulos:2013:simulation,
  author = 	 {Thomopoulos, N. T.},
  title = 	 {Essentials of Monte Carlo simulation: Statistical
                  methods for building simulation models},
  publisher = 	 {Springer},
  year = 	 2013,
  isbn = 	 {978-146146022-0},
  language = 	 {english}
}

@Article{actuar,
  author = 	 {Dutang, C and Goulet, V. and Pigeon, M.},
  title = 	 {\pkg{actuar}: An {R} Package for Actuarial Science},
  journal = 	 {Journal of Statistical Software},
  year = 	 2008,
  volume = 	 25,
  number = 	 7,
  doi = 	 {10.18637/jss.v025.i07},
  url = 	 {https://doi.org/10.18637/jss.v025.i07},
  language = 	 {english}
}

@Article{cm,
  author = 	 {Belhadj, H. and Goulet, V. and Ouellet, T.},
  title = 	 {On Parameter Estimation in Hierarchical Credibility},
  journal = 	 AB,
  year = 	 2009,
  volume =	 39,
  number =	 2,
  language =	 {english}
}

@Manual{expint,
  title = 	 {expint: Exponential Integral and Incomplete Gamma Function},
  author = 	 {Goulet, V.},
  year = 	 {2019},
  note = 	 {R package version 0.1-6},
  url = 	 {https://cran.r-project.org/package=expint},
}

@Article{statmod,
  author = 	 {Giner, G. and Smyth, G. K.},
  title = 	 {\pkg{statmod}: {P}robability calculations for the
                  inverse gaussian distribution},
  journal = 	 {{R Journal}},
  year = 	 2016,
  volume = 	 8,
  number = 	 1,
  pages = 	 {339-351},
  doi = 	 {10.32614/RJ-2016-024},
  url = 	 {https://doi.org/10.32614/RJ-2016-024},
  language = 	 {english}
}
