Modeling auto insurance frequency using K-means and mixture regression

[1] A. E. Renshaw, Modelling the Claims Process in the Presence of Covariates, ASTIN Bulletin, Vol. 24, No. 2, 265-285, (1994).
[2] A. Dempster, N. Laird, and D. Rubin, Maximum likelihood from Incomplete Data via the
EM Algorithm, Journal of the Royal Statistical Society B (Methodological), Vol. 39, No. 1,
pages 1-38, (1997).
[3] C. Akantziliotou, R. A. Rigby, and D. M. Stasinopoulos, A framework for modelling
overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution, Comput. Stat. Data Anal., 53, 381-393, (2008).
[4] S. Aryuyuen and W. Bodhisuwan, The negative binomial-generalized exponential (NB-GE)
distribution, Appl. Math. Sci., 7, 1093-1105, (2013).
[5] J. Del Castillo and M. Perez-Casany ´ , Overdispersed and underdispersed Poisson generalizations, J. Stat. Plan. Inference, 134, 486-500, (2005).
[6] T. C. Fung, A. L. Badescu, and X. S. Lin, A class of mixture of experts models for general
insurance: Application to correlated claim frequencies, ASTIN Bulletin: The Journal of the
IAA, 49(3), 647-688, (2019a).
[7] T. C. Fung, A. L. Badescu, and X. S. Lin, A class of mixture of experts models for general
insurance: Theoretical developments, Insurance: Mathematics and Economics, 89, 111-127,
(2019b).
[8] W. H. Greene, Accounting for Excess Zeros and Sample Selection in Poisson and Negative
Binomial Regression Models, Working Paper EC-94-10, Department of Economics, Stern
School of Business, New York University, (1994).
[9] G. Maclachlan and T. Krishnan, The EM Algorithm and Extensions, Wiley Series in
Probability and Statistics, 2nd edition, (2007).
[10] J. Garrido, C. Genest, and J. Schulz, Generalized linear models for dependent frequency
and severity of insurance claims, Insurance: Mathematics and Economics, 70, 205-215,
(2016).
[11] J. Hinde and C. G. B. Demetrio ´ , Overdispersion: Models and Estimation, Associacao
Brasileira de Estatistica, Sao Paulo, (1998).
[12] H. Zamani and N. Ismail, Negative Binomial-Lindley Distribution And Its Application, J.
Mathematics And Statistics, 1, 49, (2010).
[13] J. F. Lawless, Negative binomial and mixed Poisson regression, The Canadian Journal of
Statistics, Vol. 15, No. 3, Pages 209-225, (1987).
[14] D. Lukasz, L. Mathias, and M. V. Wuthrich ¨ , Gamma Mixture Density Networks and their
application to modelling insurance claim amounts, Insurance: Mathematics and Economics,
Vol. 101, Part B, Pages 240-261, (2011).
[15] L. Simon, Fitting negative binomial distribution by the method of maximum likelihood, J.
Casualty Actuarial Society, 17, 45-53, (1961).
[16] L. Breiman, J. Friedman, R. Olshen, and C. Stone, Classification and regression trees,
Wadsworth Brooks, (1984).
[17] B. G. Lindsay, Mixture Models: Theory, Geometry, and Applications, NSF-CBMS Regional
Conference Series in Probability and Statistics 5, Hayward: Institute of Mathematical Statistics, (1995).
[18] L. Breiman, Random forests, Machine Learning, 45, 5-32, (2001).
[19] M. Aitkin, D. Anderson, B. Francis, and J. Hinde, Statistical Modelling in GLIM, Oxford
University Press, New York, (1990).
[20] G. McLachlan and D. Peel, Finite Mixture Models, Wiley Series in Probability and Statistics, John Wiley and Sons Inc., (2000).
[21] M. Lichman, UCI Machine Learning Repository, http://archive.ics.uci.edu/ml, (2013).
[22] N. E. Breslow, Extra-Poisson Variation in Log-Linear Models, Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 38-44, (1984).
[23] R. Verbelen, L. Gong, K. Antonio, A. Badescu, and S. Lin, Fitting Mixtures Of Erlangs
To Censored And Truncated Data Using The EM Algorithm, ASTIN Bulletin: The Journal
of the IAA, Vol. 45, Issue 3, pp. 729-758, (2015).
[24] S. M. Goldfeld and R. E. Quandt, A Markov model for switching regressions, Journal of
Econometrics, Vol 1, Issue 1, Pages 3-15, (1973).
[25] S. C. K. Lee and X. Sheldon Lin, Modeling Dependent Risks with Multivariate Erlang
Mixtures, ASTIN Bulletin: The Journal of the IAA, Volume 42, Issue 1, pp. 153-180, (2012).
[26] P. Shi and E. A. Valdez, Multivariate negative binomial models for insurance claim counts,
Insur Math Econ 55, 1829, (2014).
[27] K. F. Sellers and A. Raim, A flexible zero-inflated model to address data dispersion, Comput. Stat. Data Anal., 99, 68-80, (2016).
[28] S. C. Tseung, A. Badescu, T. C. Fung, and X. S. Lin, LRMoE.jl: a software package for
insurance loss modelling using mixture of experts regression model, Ann. Actuar. Sci., 15(2),
419-440, (2021).
[29] W. Jiang and M. A. Tanner, On the Approximation Rate of Hierarchical Mixtures-ofExperts for Generalized Linear Models, Neural Computation, Vol 11, Issue 5, 1183-1198,
(1999).
[30] R. Winkelmann, Econometric Analysis of Count Data, Springer-Verlag, (2003).
[31] K. K. Yau, K. Wang, and A. H. Lee, Zero-Inflated Negative Binomial Mixed Regression
Modelling of Over-Dispersed Count Data with Extra Zeros, Biometrical Journal, 45, 437-452,
(2003).
[32] Z. Yang, J. W. Hardin, C. L. Addy, and Q. H. Vuong, Testing Approaches for Overdispersion in Poisson Regression versus the Generalized Poisson Model, Biometrical Journal,
49, 565-584, (2007).
[33] Y. Lv, S. Tang, and H. Zhao, Real-time Highway Traffic Accident Prediction Based on the
k-Nearest Neighbor Method, International Conference on Measuring Technology and Mechatronics Automation, pp. 547-550, (2009).
[34] H. Zamani, P. Faroughi, and N. Ismail, Bivariate generalized Poisson regression model:
applications on health care data, Empir Econ, 51(4), 1607-1621, (2016).
[35] P. Zhang, D. Pitt, and X. Wu, A new multivariate zero-inflated hurdle model with applications in automobile insurance, ASTIN Bulletin: The Journal of the IAA, 124, (2022).