Modelling insurance losses using a new beta power transformed family of distributions

References

• Adcock, C., M. Eling, and N. Loperfido. 2015. Skewed distributions in finance and actuarial science: A review. The European Journal of Finance 21 (13–14):1253–81. doi:10.1080/1351847X.2012.720269.
   Web of Science ®Google Scholar
• Al-Malki, S. J. 2014. Statistical analysis of lifetime data using new modified Weibull distributions. PhD. diss., The University of Manchester, United Kingdom.
   Google Scholar
• Artzner, P. 1999. Application of coherent risk measures to capital requirements in insurance. North American Actuarial Journal 3 (2):11–25. doi:10.1080/10920277.1999.10595795.
   Google Scholar
• Azzalini, A., T. Del Cappello, and S. Kotz. 2002. Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution 11 (3–4):2.
   Google Scholar
• Bagnato, L., and A. Punzo. 2013. Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm. Computational Statistics 28 (4):1571–1597. doi:10.1007/s00180-012-0367-4.
   Web of Science ®Google Scholar
• Calderín-Ojeda, E., and C. F. Kwok. 2016. Modeling claims data with composite Stoppa models. Scandinavian Actuarial Journal 2016 (9):817–836. doi:10.1080/03461238.2015.1034763.
   Web of Science ®Google Scholar
• Cooray, K., and M. M. Ananda. 2005. Modeling actuarial data with a composite lognormal-Pareto model. Scandinavian Actuarial Journal 2005 (5):321–334. doi:10.1080/03461230510009763.
   Google Scholar
• Cordeiro, G. M., and M. de Castro. 2011. A new family of generalized distributions. Journal of Statistical Computation and Simulation 81 (7):883–898. doi:10.1080/00949650903530745.
   Web of Science ®Google Scholar
• Demicheli, R., G. Bonadonna, W. J. Hrushesky, M. W. Retsky, and P. Valagussa. 2004. Menopausal status dependence of the timing of breast cancer recurrence after surgical removal of the primary tumour. Breast Cancer Research 6 (6):R689. doi:10.1186/bcr937.
   PubMed Web of Science ®Google Scholar
• Eling, M. 2012. Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models? Insurance: Mathematics and Economics 51 (2):239–248. doi:10.1016/j.insmatheco.2012.04.001.
   Web of Science ®Google Scholar
• Eugene, N., C. Lee, and F. Famoye. 2002. Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods 31 (4):497–512. doi:10.1081/STA-120003130.
   Web of Science ®Google Scholar
• Gomes, A. E., C. Q. Da-Silva, and G. M. Cordeiro. 2015. The exponentiated G Poisson model. Communications in Statistics - Theory and Methods 44 (20):4217–4240. doi:10.1080/03610926.2013.793351.
   Web of Science ®Google Scholar
• Gupta, R. D., and D. Kundu. 2001. Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal 43 (1):117–130. doi:10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R.
   Web of Science ®Google Scholar
• Hogg, R. V., and S. A. Klugman. 2009. Loss distributions. Probability and statistics. New York: Wiley.
   Google Scholar
• Kazemi, R., and M. Noorizadeh. 2015. A comparison between skew-logistic and skew-normal distributions. Matematika 31 (1):15–24.
   Web of Science ®Google Scholar
• Klugman, S. A., H. H. Panjer, and G. E. Willmot. 2012. Loss models: From data to decisions. Vol. 715. New York: John Wiley & Sons, Inc.
   Google Scholar
• Lai, C. D., and M. Xie. 2006. Failure time data. In Stochastic ageing and dependence for reliability, 345–362. New York: Springer.
   Google Scholar
• Landsman, Z., U. Makov, and T. Shushi. 2016. Tail conditional moments for elliptical and log-elliptical distributions. Insurance: Mathematics and Economics 71:179–188. doi:10.1016/j.insmatheco.2016.09.001.
   Web of Science ®Google Scholar
• McNeil, A. J. 1997. Estimating the tails of loss severity distributions using extreme value theory. ASTIN Bulletin 27 (1):117–137. doi:10.2143/AST.27.1.563210.
   Google Scholar
• Mudholkar, G. S., and D. K. Srivastava. 1993. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42 (2):299–302. doi:10.1109/24.229504.
   Web of Science ®Google Scholar
• Nadarajah, S., and S. A. Bakar. 2014. New composite models for the Danish fire insurance data. Scandinavian Actuarial Journal 2014 (2):180–187. doi:10.1080/03461238.2012.695748.
   Web of Science ®Google Scholar
• Nadarajah, S., G. M. Cordeiro, and E. M. Ortega. 2015. The exponentiated G geometric family of distributions. Journal of Statistical Computation and Simulation 85 (8):1634–1650. doi:10.1080/00949655.2014.885977.
   Web of Science ®Google Scholar
• Resnick, S. I. 1997. Discussion of the Danish data on large fire insurance losses. ASTIN Bulletin 27 (1):139–151. doi:10.2143/AST.27.1.563211.
   Google Scholar
• Scollnik, D. P. 2007. On composite lognormal-Pareto models. Scandinavian Actuarial Journal 2007 (1):20–33. doi:10.1080/03461230601110447.
   Google Scholar
• Scollnik, D. P., and C. Sun. 2012. Modeling with Weibull-Pareto models. North American Actuarial Journal 16 (2):260–272. doi:10.1080/10920277.2012.10590640.
   Google Scholar
• Shaw, W. T., and I. R. Buckley. 2007. The alchemy of probability distributions: Beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. ArXiv preprint arXiv: 0901.0434.
   Google Scholar
• Tahir, M. H., and G. M. Cordeiro. 2016. Compounding of distributions: A survey and new generalized classes. Journal of Statistical Distributions and Applications 3 (1):13. doi:10.1186/s40488-016-0052-1.
   Google Scholar
• Vernic, R. 2006. Multivariate skew-normal distributions with applications in insurance. Insurance: Mathematics and Economics 38 (2):413–426. doi:10.1016/j.insmatheco.2005.11.001.
   Web of Science ®Google Scholar