New methods to define heavy-tailed distributions with applications to insurance data

References

• Bhati D, Ravi S. On generalized log-Moyal distribution: a new heavy tailed size distribution. Insur Math Econ. 2018;79:247–259. doi: 10.1016/j.insmatheco.2018.02.002
   Web of Science ®Google Scholar
• Beirlant J, Matthys G, Dierckx G. Heavy-tailed distributions and rating. ASTIN Bull. 2001;31(1):37–58. doi: 10.2143/AST.31.1.993
   Google Scholar
• McNeil AJ. Estimating the tails of loss severity distributions using extreme value theory. ASTIN Bull. 1997;27(1):117–137. doi: 10.2143/AST.27.1.563210
   Google Scholar
• Resnick SI. Discussion of the Danish data on large fire insurance losses. ASTIN Bull. 1997;27(1):139–151. doi: 10.2143/AST.27.1.563211
   Google Scholar
• Eling M. Fitting insurance claims to skewed distributions: are the skew-normal and skew-student good models. Insur Math Econ. 2012;51(2):239–248. doi: 10.1016/j.insmatheco.2012.04.001
   Web of Science ®Google Scholar
• Adcock C, Eling M, Loperfido N. Skewed distributions in finance and actuarial science: a review. Eur J Financ. 2015;21(13-14):1253–1281. doi: 10.1080/1351847X.2012.720269
   Web of Science ®Google Scholar
• Shushi T. Skew-elliptical distributions with applications in risk theory. Eur Actuar J. 2017;7:277–296. doi: 10.1007/s13385-016-0144-9
   Web of Science ®Google Scholar
• Punzo A. A new look at the inverse Gaussian distribution with applications to insurance and economic data. J Appl Stat. 2019;46(7):1260–1287. doi: 10.1080/02664763.2018.1542668
   Web of Science ®Google Scholar
• Azzalini A, Del Cappello T, Kotz S. Log-skew-normal and log-skew-t distributions as models for family income data. J Inco Dist. 2002;11:12–20.
   Google Scholar
• Bagnato L, Punzo A. Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm. Comput Stat. 2013;28(4):1571–1597. doi: 10.1007/s00180-012-0367-4
   Web of Science ®Google Scholar
• Paula GA, Leiva V, Barros M, et al. Robust statistical modeling using the Birnbaum Saunders t distribution applied to insurance. Appl Stoch Models Bus Ind. 2012;28(1):16–34. doi: 10.1002/asmb.887
   Web of Science ®Google Scholar
• Klugman SA, Panjer HH, Willmot GE. Loss models: from data to decisions. 4th ed. John Wiley and Sons, Inc; 2012. (Wiley series in probability and statistics).
   Google Scholar
• Nadarajah S, Abu Bakar SA. New composite models for the Danish fire insurance data. Scand Actuar J. 2014;2014(2):180–187. doi: 10.1080/03461238.2012.695748
   Web of Science ®Google Scholar
• Bakar SA, Hamzah N, Maghsoudi M, et al. Modeling loss data using composite models. Insur Math Econ. 2015;61:146–154. doi: 10.1016/j.insmatheco.2014.08.008
   Web of Science ®Google Scholar
• Punzo A, Bagnato L, Maruotti A. Compound unimodal distributions for insurance losses. Insur Math Econ. 2018;81:95–107. doi: 10.1016/j.insmatheco.2017.10.007
   Web of Science ®Google Scholar
• Mazza A, Punzo A. Modeling household income with contaminated unimodal distributions. In: Petrucci A, Racioppi F, Verde R, editors. New statistical developments in data science; 2019. p. 373–391. (Springer proceedings in mathematics & statistics; vol. 288).
   Google Scholar
• Tahir MH, Cordeiro GM. Compounding of distributions: a survey and new generalized classes. J Stat Distrib Appl. 2016;3(1):1–35. doi: 10.1186/s40488-016-0052-1
   Google Scholar
• Bernardi M, Maruotti A, Petrella L. Skew mixture models for loss distributions: a Bayesian approach. Insur Math Econ. 2012;51(3):617–623. doi: 10.1016/j.insmatheco.2012.08.002
   Web of Science ®Google Scholar
• Miljkovic T, Grr̈n B. Modeling loss data using mixtures of distributions. Insur Math Econ. 2016;70:387–396. doi: 10.1016/j.insmatheco.2016.06.019
   Web of Science ®Google Scholar
• Punzo A, Mazza A, Maruotti A. Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions. J Appl Stat. 2018;45(14):2563–2584. doi: 10.1080/02664763.2018.1428288
   Web of Science ®Google Scholar
• Dutta K, Perry J. A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital. New Engl Econ Rev. 2006;6(13):1–85.
   Google Scholar
• Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron. 2013;71(1):63–79. doi: 10.1007/s40300-013-0007-y
   Google Scholar
• Ahmad Z, Hamedani GG, Butt NS. Recent developments in distribution theory: a brief survey and some new generalized classes of distributions. Pak J Stat Oper Res. 2019;15(1):87–110. doi: 10.18187/pjsor.v15i1.2803
   Web of Science ®Google Scholar
• Jamal F, Nasir M. Some new members of the T-X family of distributions. Proceedings of the 17th International Conference on Statistical Sciences; 2019 Jan; Lahore, Pakistan. <hal-01965176v2>.
   Google Scholar
• Mahdavi A, Kundu D. A new method for generating distributions with an application to exponential distribution. Commun Stat-Theory M. 2017;46(13):6543–6557. doi: 10.1080/03610926.2015.1130839
   Web of Science ®Google Scholar
• Glänzel W. A characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory. Dordrecht: Springer; 1987. p. 75-84.
   Google Scholar
• Glänzel W. Some consequences of a characterization theorem based on truncated moments. Statistics. 1990;21(4):613–618. doi: 10.1080/02331889008802273
   Google Scholar
• Artzner P. Application of coherent risk measures to capital requirements in insurance. N Am Actuar J. 1999;3(2):11–25. doi: 10.1080/10920277.1999.10595795
   Google Scholar
• Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42(2):299–302. doi: 10.1109/24.229504
   Web of Science ®Google Scholar
• Gupta RD, Kundu D. Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom J. 2001;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
• Haq MAU, Elgarhy M, Hashmi S. The generalized odd Burr III family of distributions: properties, applications and characterizations. J Taibah Univ Sci. 2019;13(1):961–971. doi: 10.1080/16583655.2019.1666785
   Web of Science ®Google Scholar
• Calabria R, Pulcini G. Point estimation under asymmetric loss functions for left-truncated exponential samples. Comm Statist Theory Methods. 1996;25(3):585–600. doi: 10.1080/03610929608831715
   Web of Science ®Google Scholar