141
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A survey of a hurdle model for heavy-tailed data based on the generalized lambda distribution

ORCID Icon, &
Pages 781-808 | Received 19 Apr 2018, Accepted 11 Nov 2018, Published online: 31 Dec 2018

References

  • Balasooriya, U., and C.-K. Low. 2008. Modeling insurance claims with extreme observations: transformed kernel density and generalized lambda distribution. North American Actuarial Journal 12 (2):129–42. doi:10.1080/10920277.2008.10597507.
  • Bickel, P. J., and M. Rosenblatt. 1973. On some global measures of the deviations of density function estimates. The Annals of Statistics 1 (6):1071–95. http://www.jstor.org/stable/2958266. doi:10.1214/aos/1176342558.
  • Cebrián, A. C., M. Denuit, and P. Lambert. 2003. Generalized Pareto fit to the society of actuaries large claims database. North American Actuarial Journal 7 (3):18–36. doi:10.1080/10920277.2003.10596098.
  • Corrado, C. J. 2001. Option pricing based on the generalized lambda distribution. Journal of Futures Markets 21 (3):213–36. doi:10.1002/1096-9934(200103)21:3<213::AID-FUT2>3.0.CO;2-H.
  • Couturier, D.-L., and M.-P. Victoria-Feser. 2010. Zero-inflated truncated generalized Pareto distribution for the analysis of radio audience data. The Annals of Applied Statistics 4 (4):1824–46. http://www.jstor.org/stable/23362450. doi:10.1214/10-AOAS358.
  • Cox, D. R., and N. Reid. 1987. Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society. Series B (Methodological) 49 (1):1–39. http://www.jstor.org/stable/2345476.
  • Duan, N., W. G. Manning, C. N. Morris, and J. P. Newhouse. 1983. A comparison of alternative models for the demand for medical care. Journal of Business & Economic Statistics 1 (2):115–26. doi:10.2307/1391852.
  • Dunn, P. K., and G. K. Smyth. 1996. Randomized quantile residuals. Journal of Computational and Graphical Statistics 5 (3):236–44. doi:10.2307/1390802.
  • Fan, Y. 1994. Testing the goodness of fit of a parametric density function by Kernel method. Econometric Theory 10 (2):316–56. doi:10.1017/S0266466600008434.
  • Fournier, B., N. Rupin, M. Bigerelle, D. Najjar, and A. Iost. 2006. Application of the generalized lambda distributions in a statistical process control methodology. Journal of Process Control 16 (10):1087–98. doi:10.1016/j.jprocont.2006.06.009.
  • Freimer, M., G. Kollia, G. S. Mudholkar, and C. T. Lin. 1988. A study of the generalized Tukey lambda family. Communications in Statistics-Theory and Methods 17 (10):3547–67. doi:10.1080/03610928808829820.
  • Grimshaw, S. D. 1993. Computing maximum likelihood estimates for the generalized Pareto distribution. Technometrics 35 (2):185–91. doi:10.1080/00401706.1993.10485040.
  • Hastings, C., F. Mosteller, J. W. Tukey, and C. P. Winsor. 1947. Low moments for small samples: A comparative study of order statistics. The Annals of Mathematical Statistics 18 (3):413–26. http://www.jstor.org/stable/2235737. doi:10.1214/aoms/1177730388.
  • Hilbe, J. 2009. Logistic regression models. Abingdon, UK: Taylor & Francis. https://books.google.com.br/books?id=eJcMIAAACAAJ.
  • Hosking, J. R., and J. R. Wallis. 1987. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29 (3):339–49. doi:10.2307/1269343.
  • Hyndman, R. J., and Y. Fan. 1996. Sample quantiles in statistical packages. The American Statistician 50 (4):361–5. doi:10.2307/2684934.
  • Jones, A. M., J. Lomas, and N. Rice. 2014. Going beyond the mean in healthcare cost regressions: A comparison of methods for estimating the full conditional distribution (Technical Report). HEDG, c/o Department of Economics, University of York.
  • Karian, Z. A., and E. J. Dudewicz. 1999. Fitting the generalized lambda distribution to data: a method based on percentiles. Communications in Statistics-Simulation and Computation 28 (3):793–819. doi:10.1080/03610919908813579.
  • Karian, Z. A., and E. J. Dudewicz. 2000. Fitting statistical distributions: The generalized lambda distribution and generalized bootstrap methods. Boca Raton, FL: CRC Press.
  • Karian, Z. A., and E. J. Dudewicz. 2003. Comparison of GLD fitting methods: Superiority of percentile fits to moments in l2 norm. Journal of the Iranian Statistical Society 2 (2):171–87.
  • Karian, Z. A., E. J. Dudewicz, and P. Mcdonald. 1996. The extended generalized lambda distribution system for fitting distributions to data: History, completion of theory, tables, applications, the” final word” on moment fits. Communications in Statistics-Simulation and Computation 25 (3):611–42. doi:10.1080/03610919608813333.
  • King, R. A., and H. MacGillivray. 1999. A starship estimation method for the generalized lambda distributions. Australian & New Zealand Journal of Statistics 41 (3):353–74. doi:10.1111/1467-842X.00089.
  • Lakhany, A., and H. Mausser. 2000. Estimating the parameters of the generalized lambda distribution. ALGO Research Quarterly 3 (3):47–58.
  • Lambert, D. 1992. Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics 34 (1):1–14. doi:10.2307/1269547.
  • Mihaylova, B., A. Briggs, A. O’Hagan, and S. G. Thompson. 2011. Review of statistical methods for analysing healthcare resources and costs. Health Economics 20 (8):897–916. doi:10.1002/hec.1653.
  • Mullahy, J. 1986. Specification and testing of some modified count data models. Journal of Econometrics 33 (3):341–65. doi:10.1016/0304-4076(86)90002-3.
  • Nelder, J. A., and R. J. Baker. 1972. Generalized linear models. Hoboken, NJ: Wiley Online Library.
  • Nelder, J. A., and R. Mead. 1965. A simplex method for function minimization. The Computer Journal 7 (4):308–13. doi:10.1093/comjnl/7.4.308.
  • Öztürk, A., and R. Dale. 1982. A study of fitting the generalized lambda distribution to solar radiation data. Journal of Applied Meteorology 21 (7):995–1004. doi:10.1175/1520-0450(1982)021<0995:ASOFTG >2.0.CO;2.
  • Öztürk, A., and R. F. Dale. 1985. Least squares estimation of the parameters of the generalized lambda distribution. Technometrics 27 (1):81–4. doi:10.2307/1270473.
  • Pal, S. 2004. Evaluation of nonnormal process capability indices using generalized lambda distribution. Quality Engineering 17 (1):77–85. doi:10.1081/QEN-200028709.
  • Pickands, J. 1975. Statistical inference using extreme order statistics. The Annals of Statistics 3 (1):119–31. http://www.jstor.org/stable/2958083.
  • R Core Team. 2017. R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria: R: The R Foundation. https://www.R-project.org/.
  • Ramberg, J. S., and B. W. Schmeiser. 1974. An approximate method for generating asymmetric random variables. Communications of the ACM 17 (2):78–82. doi:10.1145/360827.360840.
  • Rigby, R. A., and D. M. Stasinopoulos. 2005. Generalized additive models for location, scale and shape (with discussion). Journal of the Royal Statistical Society: Series C (Applied Statistics) 54:507–54. doi:10.1111/j.1467-9876.2005.00510.x.
  • Sheather, S. J., and M. C. Jones. 1991. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological) 53 (3):683–90.
  • Silverman, B. W. 1986. Density estimation for statistics and data analysis. Vol. 26. Boca Raton, FL: CRC Press.
  • Su, S. 2005. A discretized approach to flexibly fit generalized lambda distributions to data. Journal of Modern Applied Statistical Methods 4 (2):7.
  • Su, S. 2007a. Fitting single and mixture of generalized lambda distributions to data via discretized and maximum likelihood methods: GLDEX in R. Journal of Statistical Software 21 (9):1–17.
  • Su, S. 2007b. Numerical maximum log likelihood estimation for generalized lambda distributions. Computational Statistics & Data Analysis 51 (8):3983–98. doi:10.1016/j.csda.2006.06.008.
  • Su, S. 2011. Maximum log likelihood estimation using em algorithm and partition maximum log likelihood estimation for mixtures of generalized lambda distributions. Journal of Modern Applied Statistical Methods 10 (2):17.
  • Su, S. 2015. Flexible parametric quantile regression model. Statistics and Computing 25 (3):635–50. doi:10.1007/s11222-014-9457-1.
  • Su, S. 2016. Fitting flexible parametric regression models with GLDreg in R. Journal of Modern Applied Statistical Methods 15 (2):46.
  • Tarsitano, A. 2004. Fitting the generalized lambda distribution to income data. COMPSTAT 2004 symposium, 1861–7.
  • Tukey, J. W. 1990. Practical relationship between the common transformations of percentages or fractions and of amounts. The Collected Works of John W. Tukey, Volume VI: More Mathematical, 211–9.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.