A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting

References

• M. Aboraya, M.M. Ali, H.M. Yousof, and M. Ibrahim, A new flexible probability model: Theory, estimation and modeling bimodal left skewed data, Pak. J. Stat. Oper. Res. 18 (2022), pp. 437–463.
   Web of Science ®Google Scholar
• C. Acerbi and D. Tasche, On the coherence of expected shortfall, J. Bank. Financ. 26 (2002), pp. 1487–1503.
   Web of Science ®Google Scholar
• K. Aidi, N.S. Butt, M.M. Ali, M. Ibrahim, H.M. Yousof, and W.A.M. Shehata, A modified chi-square type test statistic for the double burr X model with applications to right censored medical and reliability data, Pak. J. Stat. Oper. Res. 17 (2021), pp. 615–623.
   Web of Science ®Google Scholar
• E. Altun, M. Alizadeh, H.M. Yousof, and G.G. Hamedani, The Gudermannian generated family of distributions with characterizations, regression models and applications, Studia Sci. Math. Hung. 59 (2022), pp. 93–115.
   Web of Science ®Google Scholar
• P. Artzner, Application of coherent risk measures to capital requirements in insurance, N. Am. Actuar. J. 3 (1999), pp. 11–25.
   Google Scholar
• J. Beirlant, E. Joossens, and J. Segers, Generalized Pareto fit to the society of actuaries large claims database, N. Am. Actuar. J. 8 (2004), pp. 108–111.
   Google Scholar
• J. Beran, D. Schell, and M. Stehlík, The harmonic moment tail index estimator: Asymptotic distribution and robustness, Ann. Inst. Stat. Math. 66 (2014), pp. 193–220.
   Web of Science ®Google Scholar
• A. Charpentier, Computational Actuarial Science with R, CRC press, 2014.
   Google Scholar
• Y.P. Chaubey and R. Zhang, An extension of Chen's family of survival distributions with bathtub shape or increasing hazard rate function, Commun. Stat.-Theor. Meth. 44 (2015), pp. 4049–4064.
   Web of Science ®Google Scholar
• Z. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Stat. Probab. Lett. 49 (2000), pp. 155–161.
   Web of Science ®Google Scholar
• G.M. Cordeiro, A.Z. Afify, H.M. Yousof, R.R. Pescim, and G.R. Aryal, The exponentiated Weibull-H family of distributions: Theory and applications, Mediterr. J. Math. 14 (2017), pp. 155.
   Web of Science ®Google Scholar
• A. De Myttenaere, B. Golden, B. Le Grand, and F. Rossi, Mean absolute percentage error for regression models, Neurocomputing. 192 (2016), pp. 38–48.
   Web of Science ®Google Scholar
• S. Dey, D. Kumar, P.L. Ramos, and F. Louzada, Exponentiated Chen distribution: Properties and estimation, Commun. Stat.-Simul. Comput. 46 (2017), pp. 8118–8139.
   Web of Science ®Google Scholar
• F. Figueiredo, M.I. Gomes, and L. Henriques-Rodrigues, Value-at-risk estimation and the PORT mean-of-order-p methodology, Revstat. 15 (2017), pp. 187–204.
   Web of Science ®Google Scholar
• E. Furman and Z. Landsman, Tail variance premium with applications for elliptical portfolio of risks, ASTIN Bulletin. 36 (2006), pp. 433–462.
   Web of Science ®Google Scholar
• H. Goual and H.M. Yousof, Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test, J. Appl. Stat. 47 (2020), pp. 393–423.
   PubMed Web of Science ®Google Scholar
• H. Goual, H.M. Yousof, and M.M. Ali, Validation of the odd Lindley exponentiated exponential by a modified goodness of fit test with applications to censored and complete data, Pak. J. Stat. Oper. Res. 15 (2019), pp. 745–771.
   Web of Science ®Google Scholar
• R.V. Hogg and S.A. Klugman, Loss Distributions, John Wiley & Sons, Inc., New York, 1984.
   Google Scholar
• R. Ibragimov and A. Prokhorov, Heavy Tails and Copulas: Topics in Dependence Modelling in Economics and Finance, World Scientific, Singapore, 2017.
   Google Scholar
• M. Ibrahim, K. Aidi, M.M. Ali, and H.M. Yousof, The exponential generalized log-logistic model: Bagdonavičius–Nikulin test for validation and non-Bayesian estimation methods, Commun. Stat. Appl. Meth. 29 (2021), pp. 681–705.
   Web of Science ®Google Scholar
• M. Ibrahim, K. Aidi, M.M. Ali, and H.M. Yousof, A novel test statistic for right censored validity under a new Chen extension with applications in reliability and medicine, Annals of Data Science Forthcoming. (2022), doi: 10.1007/s40745-022-00416-6.
   Google Scholar
• M. Ibrahim, A.S. Yadav, H.M. Yousof, H. Goual, and G.G. Hamedani, A new extension of Lindley distribution: Modified validation test, characterizations and different methods of estimation, Commun. Stat. Appl. Meth. 26 (2019), pp. 473–495.
   Web of Science ®Google Scholar
• F. Jan, I. Shah, and S. Ali, Short-term electricity prices forecasting using functional time series analysis, Energies. 15 (2022), pp. 3423.
   Web of Science ®Google Scholar
• M. Ç. Korkmaz, E. Altun, C. Chesneau, and H.M. Yousof, On the unit-Chen distribution with associated quantile regression and applications, Mathematica Slovaca. 72 (2022), pp. 765–786.
   Web of Science ®Google Scholar
• Z. Landsman, On the tail mean–variance optimal portfolio selection, Insur. Math. Econ. 46 (2010), pp. 547–553.
   Web of Science ®Google Scholar
• M.N. Lane, Pricing risk transfer transactions 1, ASTIN Bull. J. IAA. 30 (2000), pp. 259–293.
   Google Scholar
• M. Mansour, M. Rasekhi, M. Ibrahim, K. Aidi, H.M. Yousof, and E.A. Elrazik, A new parametric life distribution with modified Bagdonavičius–Nikulin goodness-of-fit test for censored validation, properties, applications, and different estimation methods, Entropy. 22 (2020), pp. 592.
   PubMed Web of Science ®Google Scholar
• W.A.M. Shehata and H.M. Yousof, The four-parameter exponentiated Weibull model with Copula, properties and real data modeling, Pak. J. Stat. Oper. Res. 17 (2021), pp. 649–667.
   Web of Science ®Google Scholar
• W.A.M. Shehata and H.M. Yousof, A novel two-parameter Nadarajah–Haghighi extension: Properties, copulas, modeling real data and different estimation methods, Stat. Optim. Inf. Comput. 10 (2022), pp. 725–749.
   Google Scholar
• W.A.M. Shehata, H.M. Yousof, and M. Aboraya, A novel generator of continuous probability distributions for the asymmetric left-skewed bimodal real-life data with properties and copulas, Pak. J. Stat. Oper. Res. 17 (2021), pp. 943–961.
   Web of Science ®Google Scholar
• M. Stehlík, R. Potocký, H. Waldl, and Z. Fabián, On the favorable estimation for fitting heavy tailed data, Comput. Stat. 25 (2010), pp. 485–503.
   Web of Science ®Google Scholar
• J.D. Stein, F. Lum, P.P. Lee, W.L. Rich III, and A.L. Coleman, Use of health care claims data to study patients with ophthalmologic conditions, Ophthalmology. 121 (2014), pp. 1134–1141.
   PubMed Web of Science ®Google Scholar
• D. Tasche, Expected shortfall and beyond, J. Bank. Financ. 26 (2002), pp. 1519–1533.
   Web of Science ®Google Scholar
• J. Wirch, Raising value at risk, N. Am. Actuar. J. 3 (1999), pp. 106–115.
   Google Scholar
• A.S. Yadav, S. Shukla, H. Goual, M. Saha, and H.M. Yousof, Validation of xgamma exponential model via Nikulin–Rao–Robson goodness-of-fit test under complete and censored sample with different methods of estimation, Stat., Optim. Inf. Comput. 10 (2022), pp. 457–483.
   Google Scholar
• H.M. Yousof, A.H. Al-nefaie, K. Aidi, M.M. Ali, and M. Ibrahim, A modified Chi-square type test for distributional validity with applications to right censored reliability and medical data: A modified Chi-square type test, Pak. J. Stat. Oper. Res. 17 (2021), pp. 1113-–1121.
   Web of Science ®Google Scholar
• H.M. Yousof, M. Ç. Korkmaz, and M. Ibrahim, A novel Chen extension: Theory, characterizations and different estimation methods, Eur. J. Stat. 2 (2022), pp. 1–20.
   Google Scholar