From grouped to de-grouped data: a new approach in distribution fitting for grouped data

References

• Heitjan D. Inference from grouped continuous data: a review. Stat sci. 1989;4:164–179. doi: 10.1214/ss/1177012601
   Google Scholar
• Klugman SA, Panjer HH, Willmot GE. Loss models: from data to decisions. 4th ed. Hobuken (NJ): John Wiley & Sons; 2012.
   Google Scholar
• Current Population Survey AS, (ASEC) E. Hinc-06. Income distribution to $250,000 or more for households; 2016.
   Google Scholar
• Aghevli B, Mehran F. Optimal grouping of income distribution data. J Am Stat Assoc. 1981;76(373):22–26. doi: 10.1080/01621459.1981.10477596
   Web of Science ®Google Scholar
• Laurencelle L, Frigon JY, Châtillon G. Difference between the mean calculated from raw data and from a frequency distribution: a new approach. J Stat Comput Simul. 1992;41(3–4):201–218. doi: 10.1080/00949659208811401
   Google Scholar
• Adamidis K, Loukas S. Ml estimation in the poisson binomial distribution with grouped data via the EM algorithm. J Stat Comput Simul. 1993;45(1–2):33–39. doi: 10.1080/00949659308811470
   Web of Science ®Google Scholar
• Victoria-Feser M, Ronchetti E. Robust estimation for grouped data. J Am Stat Assoc. 1997;92(437):333–340. doi: 10.1080/01621459.1997.10473631
   Web of Science ®Google Scholar
• Qian L, Correa J. Estimation of weibull parameters for grouped data with competing risks. J Stat Comput Simul. 2003;73(4):261–275. doi: 10.1080/0094965021000033431
   Web of Science ®Google Scholar
• Xu S. Asymmetric kernel density estimation based on grouped data with applications to loss model. Commun Stat Simul Comput. 2014;43(3):657–672. doi: 10.1080/03610918.2012.712184
   Web of Science ®Google Scholar
• Huang J, Wang X, Wu X, et al. Estimation of a probability density function using interval aggregated data. J Stat Comput Simul. 2016;86(15):3093–3105. doi: 10.1080/00949655.2016.1150481
   Web of Science ®Google Scholar
• Calderín-Ojeda E, Kwok CF. Modeling claims data with composite stoppa models. Scand Actuar J. 2016;2016(9):817–836. doi: 10.1080/03461238.2015.1034763
   Web of Science ®Google Scholar
• Miljkovic T, Grün B. Modeling loss data using mixtures of distributions. Insurance: Math Econ. 2016;70:387–396.
   Web of Science ®Google Scholar
• Brazauskas V, Serfling R. Favorable estimators for fitting pareto models: a study using goodness-of-fit measures with actual data. ASTIN Bull. 2003;33(2):365–381. doi: 10.1017/S0515036100013519
   Google Scholar
• Henry J, Hsieh P. Extreme value analysis for partitioned insurance losses. Variance. 2009;3(2):214–238.
   Google Scholar
• Tillé Y, Langel M. Histogram-based interpolation of the lorenz curve and gini index for grouped data. Am Stat. 2012;66(4):225–231. doi: 10.1080/00031305.2012.734197
   Web of Science ®Google Scholar
• Lorenz MO. Methods of measuring the concentration of wealth. Publ Am Stat Assoc. 1905;9(70):209–219.
   Google Scholar
• Gini C. Sulla misura della concentrazione e della variabilità dei caratteri. Atti del R Istituto Veneto di SLA. 1914;73:1203–1248.
   Google Scholar
• Lyon M, Cheung LC, Gastwirth JL. The advantages of using group means in estimating the lorenz curve and gini index from grouped data. Am Stat. 2016;70(1):25–32. doi: 10.1080/00031305.2015.1105152
   Web of Science ®Google Scholar
• Cohen A, Sanborn A, Shiffrin R. Model evaluation using grouped or individual data. Psychon Bull Rev. 2005;15(4):697–712.
   Google Scholar
• Bermúdez S, Blanquero R. Optimization models for degrouping population data. Popul Stud (Camb). 2016;70(2):259–272. doi: 10.1080/00324728.2016.1158853
   PubMed Web of Science ®Google Scholar
• Kostaki A, Lanke J. Degrouping mortality data for the elderly. Math Popul Stud. 2000;7(4):331–341. doi: 10.1080/08898480009525465
   Google Scholar
• Wengrzik J, Timm J. Comparing several methods to fit finite mixture models to grouped data by the em algorithm. In Proceedings of the World Congress on Engineering. 2011;1(1).
   Google Scholar
• Dutang C, Goulet V, Pigeon M. actuar: an R package for actuarial science. J Stat Softw. 2008;25(7):1–37. Available from: http://www.jstatsoft.org/v25/i07/.
   Web of Science ®Google Scholar
• Macdonald P. mixdist: finite mixture distribution models; 2015. R package version 0.5-4; Available from: https://ms.mcmaster.ca/peter/mix/mix.html.
   Google Scholar
• R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2016. Available from: https://www.R-project.org/.
   Google Scholar
• Cochran WG, Cox GM. Experimental designs. New York (NY): John Wiley and Sons; 1950.
   Google Scholar
• Bartlett MS. Properties of sufficiency and statistical tests. Proc R Soc Lond A. 1937;160(901):268–282. doi: 10.1098/rspa.1937.0109
   Google Scholar
• Levene H. Robust tests for equality of variances. Contributions to probability and statistics. Essays in honor of Harold Hotelling. Redwood City (CA): Stanford University Press; 1961. p. 279–292.
   Google Scholar
• Brown MB, Forsythe AB. Robust tests for the equality of variances. J Am Stat Assoc. 1974;69(346):364–367. doi: 10.1080/01621459.1974.10482955
   Web of Science ®Google Scholar
• Patrik G. Estimating casualty insurance loss amount distributions. Proc Casualty Actuarial Soc. 1980;67:57–109.
   Google Scholar
• Lee SC, Lin XS. Modeling and evaluating insurance losses via mixtures of erlang distributions. N Am Actuar J. 2010;14(1):107–130. doi: 10.1080/10920277.2010.10597580
   Google Scholar
• Bakar SAA, Hamzaha NA, Maghsoudia M, et al. Modeling loss data using composite models. Insurance: Math Econ. 2015;61:146–154.
   Web of Science ®Google Scholar
• Bermúdez LKD. A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking. Comput Stat Data Anal. 2012;56(12):3988–3999. doi: 10.1016/j.csda.2012.05.016
   Web of Science ®Google Scholar
• Miljkovic T, SenGupta I. A new analysis of vix using mixture of regressions: examination and short-term forecasting for the s & p 500 market. High Frequency. 2018;1(1):53–65. doi: 10.1002/hf2.10009
   Google Scholar
• Miljkovic T, Fernández D. On two mixture-based clustering approaches used in modeling an insurance portfolio. Risks. 2018;6(2):57. doi: 10.3390/risks6020057
   Web of Science ®Google Scholar
• Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM-algorithm. J R Stat Soc B. 1977;39:1–38.
   Google Scholar
• McLachlan S, Peel D. Finite mixture models. Hobuken (NJ): John Wiley & Sons; 2000.
   Google Scholar
• Akaike H. A new look at the statistical model identification. IEEE Trans Automatic Control. 1974;19(6):716–723. doi: 10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• Schwarz G, et al. Estimating the dimension of a model. Ann Statist. 1978;6(2):461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• Sekhon JS. Multivariate and propensity score matching with balance optimization. Retrieved June. 2007.
   Google Scholar
• Pigeon M, Denuit M. Composite lognormal–pareto model with random threshold. Scand Actuar J. 2011;2011(3):177–192. doi: 10.1080/03461231003690754
   Web of Science ®Google Scholar
• Scollnik DP, Sun C. Modeling with weibull-pareto models. N Am Actuar J. 2012;16(2):260–272. doi: 10.1080/10920277.2012.10590640
   Google Scholar
• Punzo A, Bagnato L, Maruotti A. Compound unimodal distributions for insurance losses. Insurance: Math Econ. 2017;81:95–107.
   Web of Science ®Google Scholar