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Generalized Additive Models for Location Scale and Shape (GAMLSS) in R

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  • D. Mikis Stasinopoulos
  • Robert A. Rigby
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    Abstract

    GAMLSS is a general framework for fitting regression type models where the distribution of the response variable does not have to belong to the exponential family and includes highly skew and kurtotic continuous and discrete distribution. GAMLSS allows all the parameters of the distribution of the response variable to be modelled as linear/non-linear or smooth functions of the explanatory variables. This paper starts by defining the statistical framework of GAMLSS, then describes the current implementation of GAMLSS in R and finally gives four different data examples to demonstrate how GAMLSS can be used for statistical modelling.

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    Bibliographic Info

    Article provided by American Statistical Association in its journal Journal of Statistical Software.

    Volume (Year): 23 ()
    Issue (Month): i07 ()
    Pages:

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    Handle: RePEc:jss:jstsof:23:i07

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    References

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    1. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554.
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    Cited by:
    1. Luo, Jiawen & Chen, Langnan & Liu, Hao, 2013. "Distribution characteristics of stock market liquidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6004-6014.
    2. Bortoluzzo, Adriana B. & Claro, Danny P. & Caetano, Marco Antonio L. & Artes, Rinaldo, 2009. "Estimating Claim Size and Probability in the Auto-insurance Industry: the Zero-adjusted Inverse Gaussian (ZAIG) Distribution," Insper Working Papers wpe_175, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    3. Cordeiro, Gauss M. & Andrade, Marinho G. & de Castro, Mário, 2009. "Power series generalized nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1155-1166, February.
    4. I. Gijbels & I. Prosdocimi & G. Claeskens, 2010. "Nonparametric estimation of mean and dispersion functions in extended generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(3), pages 580-608, November.
    5. Claro, Danny P., 2009. "Estimating claim size and probability in the auto-insurance industry: the zeroadjusted Inverse Gaussian (ZAIG) distribution," Insper Working Papers wpe_159, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    6. Serinaldi, Francesco & Kilsby, Chris G., 2013. "On the sampling distribution of Allan factor estimator for a homogeneous Poisson process and its use to test inhomogeneities at multiple scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1080-1089.
    7. Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn, 2013. "A zero-adjusted gamma model for mortgage loan loss given default," International Journal of Forecasting, Elsevier, vol. 29(4), pages 548-562.
    8. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    9. Simon Jackman & Christian Kleiber & Achim Zeileis, 2007. "Regression Models for Count Data in R," Working papers 2007/24, Faculty of Business and Economics - University of Basel.
    10. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    11. Komlos, John & Brabec, Marek, 2011. "The trend of BMI values of US adults by deciles, birth cohorts 1882-1986 stratified by gender and ethnicity," Economics & Human Biology, Elsevier, vol. 9(3), pages 234-250, July.
    12. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, University of Innsbruck.
    13. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    14. Wong, Albert & Wouterse, Bram & Slobbe, Laurentius C.J. & Boshuizen, Hendriek C. & Polder, Johan J., 2012. "Medical innovation and age-specific trends in health care utilization: Findings and implications," Social Science & Medicine, Elsevier, vol. 74(2), pages 263-272.
    15. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 225-249.

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