Loss modeling with many-parameter distributions

References

• Bakar S., Hamzah N., Maghsoudi M. & Nadarajah S. (2015). Modeling loss data using composite models. Insurance: Mathematics and Economics 61, 146–154.
   Web of Science ®Google Scholar
• Beirlant J., Teugels J. & Vynckier P. (1996). Practical analysis of extreme values. Leuven University Press.
   Google Scholar
• Bølviken E. (2014). Computation and modelling in insurance and finance. Cambridge University Press.
   Google Scholar
• Box G. & Cox D. (1964). An analysis of transformations (with discussion). Journal of the Royal Statistical Society Series B 26, 231–252.
   Google Scholar
• Burr I. J. (1942). Cumulative frequency functions. Annals of Mathematical Statistics 13, 215–232.
   Google Scholar
• Chan J. S. K., Choy S. T. B., Makov U. R. & Landsman Z. (2018). Modelling insurance losses using contaminated, generalized beta type II distributions. ASTIN Bulletin 48(02), 871–904.
   Google Scholar
• Cooray K. & Ananda M. M. A. (2005). Modeling actuarial data with composite lognormal-Pareto model. Scandinavian Actuarial Journal 2005, 642–660.
   Google Scholar
• Cummins J. D., Dionne G., MacDonald J. B. & Pritchett B. M. (1990). Applications of the GB2 family of distributions in modeling insurance loss processes. Insurance: Mathematics and Economics 9(4), 257–272.
   Web of Science ®Google Scholar
• Embrechts P., Klüppelberg C. & Mikosch T. (Modelling extremal events. Stochastic Modelling and Applied Probability.1997). Springer Verlag.
   Google Scholar
• Gui W., Huang R. & Lin X. S. (2021). Fitting multivariate Erlang mixtures to data: a roughness penality approach. Journal of Computational and Applied Mathematics 386, 113216.
   Web of Science ®Google Scholar
• Hoeting J. A., Madigan D., Raftery A. E. & Volinsky C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science 14(4), 382–401.
   Web of Science ®Google Scholar
• Huber P. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the Fifth Berkely Symposium in Mathematical Statistics and Probability. University of California Press.
   Google Scholar
• Kleiber C. & Kotz S. (2003). Statistical size distributions in economics and actuarial sciences. Wiley.
   Google Scholar
• Lee S. & Lin X. (2010). Modeling and evaluating insurance losses via mixtures of Erlang distributions. North American Actuarial Journal 14(1), 107–130.
   Google Scholar
• Marlin P. (1984). Fitting the log-normal distribution to loss data subject to multiple deductibles. The Journal of Risk and Insurance 51( 4), 687–701.
   Web of Science ®Google Scholar
• Miljkovic T. & Grün B. (2016). Modeling loss data using mixtures of distributions. Insurance: Mathematics and Economics 70, 387–396.
   Web of Science ®Google Scholar
• Omari C. O., Nyambura S. G. & Mwangi J. M. W. (2018). Modeling the frequency and severity of auto insurance claims using statistical distributions. Journal of Mathematical Finance 8(1), 137–160.
   Google Scholar
• Reynkens T., Verbelen R., Beirlant J. & Antonio K. (2017). Modelling censored losses using splicing: a global fit strategy with mixed Erlang and extreme value distributions. Insurance Mathematics & Economics 77, 65–77.
   Web of Science ®Google Scholar
• Scollnik D. P. M. (2007). On composite lognormal-Pareto distributions. Scandinavian Actuarial Journal2007(1), 20–33.
   Google Scholar
• Scollnik D. P. M. & Sun C. (2012). Modelling with Weibull-Pareto models. North American Actuarial Journal 16(2), 260–272.
   Google Scholar
• Scott P. W. (1992). Multivariate density estimation: theory, practice and visualization. John Wiley & Sons.
   Google Scholar
• Venter C. (1985). Transformed Beta and Gamma distributions and aggregate losses. Casually Actuarial Society 70, 156–193.
   Google Scholar
• Verbelen R., Gong L., Antonio K., Badescu A. & Lin S. (2015). Fitting extremes of Erlangs to censored and truncated data using the EM algorithm. ASTIN Bulletin 45, 729–758.
   Web of Science ®Google Scholar
• White H. (1982). Maximum likelihood estimation of misspecified models. Econometrica 50(1), 1–25.
   Web of Science ®Google Scholar
• White H. (1994). Estimation, inference and specification analysis. Cambridge: Cambridge University Press.
   Google Scholar
• Zuanetti D. & Diniz C. (2006). A lognormal model for insurance claims data. REVSTAT – Statistical Journal 4, 131–142.
   Google Scholar