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Univariate Continuous Distributions

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Vector Generalized Linear and Additive Models

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

This chapter enumerates those univariate continuous distributions currently represented as VGLMs/VGAMs and implemented in VGAM. Most are grouped and tabulated according to their support, and/or the distribution from which they are derived (e.g., beta-type, gamma-type), and/or their purpose (e.g., statistical size distributions, actuarial distributions).

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References

  • Ahsanullah, M. H. and G. G. Hamedani 2010. Exponential Distribution: Theory and Methods. New York: Nova Science.

    Google Scholar 

  • Arnold, B. C. 2015. Pareto Distributions (Second ed.). Boca Raton: Chapman & Hall/CRC.

    MATH  Google Scholar 

  • Azzalini, A. 2014. The Skew-normal and Related Families. Cambridge: Cambridge University Press.

    Google Scholar 

  • Balakrishnan, N. and A. P. Basu (Eds.) 1995. The Exponential Distribution: Theory, Methods, and Applications. Amsterdam: Gordon and Breach.

    MATH  Google Scholar 

  • Balakrishnan, N. and C.-D. Lai 2009. Continuous Bivariate Distributions (Second ed.). New York: Springer.

    MATH  Google Scholar 

  • Balakrishnan, N. and V. B. Nevzorov 2003. A Primer on Statistical Distributions. New York: Wiley-Interscience.

    Book  MATH  Google Scholar 

  • Bowman, K. O. and L. R. Shenton 1988. Properties of Estimators for the Gamma Distribution. New York: Marcel Dekker.

    MATH  Google Scholar 

  • Chotikapanich, D. (Ed.) 2008. Modeling Income Distributions and Lorenz Curves. New York: Springer.

    MATH  Google Scholar 

  • Consul, P. C. and F. Famoye 2006. Lagrangian Probability Distributions. Boston: Birkhäuser.

    MATH  Google Scholar 

  • Everitt, B. S. and D. J. Hand 1981. Finite Mixture Distributions. London: Chapman & Hall.

    Book  MATH  Google Scholar 

  • Forbes, C., M. Evans, N. Hastings, and B. Peacock 2011. Statistical Distributions (fouth ed.). Hoboken: John Wiley & Sons.

    MATH  Google Scholar 

  • Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. New York: Springer.

    MATH  Google Scholar 

  • Gupta, A. K. and S. Nadarajah (Eds.) 2004. Handbook of Beta Distribution and Its Applications. New York, USA: Marcel Dekker.

    MATH  Google Scholar 

  • Harper, W. V., T. G. Eschenbach, and T. R. James 2011. Concerns about maximum likelihood estimation for the three-parameter Weibull distribution: Case study of statistical software. American Statistician 65(1):44–54.

    Article  Google Scholar 

  • Joe, H. 2014. Dependence Modeling with Copulas. Boca Raton, FL, USA: Chapman & Hall/CRC.

    Google Scholar 

  • Johnson, N. L., S. Kotz, and N. Balakrishnan 1994. Continuous Univariate Distributions (Second ed.), Volume 1. New York, USA: Wiley.

    Google Scholar 

  • Johnson, N. L., S. Kotz, and N. Balakrishnan 1995. Continuous Univariate Distributions (Second ed.), Volume 2. New York, USA: Wiley.

    Google Scholar 

  • Jones, M. C. 2009. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Methodology 6(1):70–81.

    Article  MATH  MathSciNet  Google Scholar 

  • Jørgensen, B. 1997. The Theory of Dispersion Models. London: Chapman & Hall.

    Google Scholar 

  • Kaas, R., M. Goovaerts, J. Dhaene, and M. Denuit 2008. Modern Actuarial Risk Theory Using R (Second ed.). Berlin: Springer.

    Book  MATH  Google Scholar 

  • Kleiber, C. and S. Kotz 2003. Statistical Size Distributions in Economics and Actuarial Sciences. Hoboken, NJ, USA: Wiley-Interscience.

    Book  MATH  Google Scholar 

  • Klugman, S. A., H. H. Panjer, and G. E. Willmot 2012. Loss Models: From Data to Decisions (4th ed.). Hoboken, NJ, USA: Wiley.

    Google Scholar 

  • Klugman, S. A., H. H. Panjer, and G. E. Willmot 2013. Loss Models: Further Topics. Hoboken, NJ, USA: Wiley.

    Book  Google Scholar 

  • Kotz, S., T. J. Kozubowski, and K. Podgórski 2001. The Laplace Distribution and Generalizations: a Revisit with Applications to Communications, Economics, Engineering, and Finance. Boston, MA, USA: Birkhäuser.

    Book  Google Scholar 

  • Kotz, S. and J. R. van Dorp 2004. Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications. Singapore: World Scientific.

    Book  Google Scholar 

  • Kozubowski, T. J. and S. Nadarajah 2010. Multitude of Laplace distributions. Statistical Papers 51(1):127–148.

    Article  MATH  MathSciNet  Google Scholar 

  • Lawless, J. F. 2003. Statistical Models and Methods for Lifetime Data (Second ed.). Hoboken, NJ, USA: John Wiley & Sons.

    MATH  Google Scholar 

  • Leemis, L. M. and J. T. McQueston 2008. Univariate distribution relationships. American Statistician 62(1):45–53.

    Article  MathSciNet  Google Scholar 

  • Lehmann, E. L. and G. Casella 1998. Theory of Point Estimation (Second ed.). New York, USA: Springer.

    MATH  Google Scholar 

  • Libby, D. L. and M. R. Novick 1982. Multivariate generalized beta distributions with applications to utility assessment. Journal of Educational and Statistics 7(4):271–294.

    Article  Google Scholar 

  • Lindsay, B. G. 1995. Mixture Models: Theory, Geometry and Applications, Volume 5. Hayward CA, USA: NSF-CBMS Regional Conference Series in Probability and Statistics, IMS.

    Google Scholar 

  • Mai, J.-F. and M. Scherer 2012. Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications. London: Imperial College Press.

    Book  Google Scholar 

  • Marshall, A. W. and I. Olkin 2007. Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. New York, USA: Springer.

    Google Scholar 

  • McCullagh, P. 1989. Some statistical properties of a family of continuous univariate distributions. Journal of the American Statistical Association 84(405):125–129.

    Article  MATH  MathSciNet  Google Scholar 

  • McLachlan, G. J. and D. Peel 2000. Finite Mixture Models. New York, USA: Wiley.

    Book  MATH  Google Scholar 

  • Murthy, D. N. P., M. Xie, and R. Jiang 2004. Weibull Models. Hoboken, NJ, USA: Wiley.

    MATH  Google Scholar 

  • Nadarajah, S. and S. A. A. Bakar 2013. A new R package for actuarial survival models. Computational Statistics 28(5):2139–2160.

    Article  MATH  MathSciNet  Google Scholar 

  • Nelsen, R. B. 2006. An Introduction to Copulas (Second ed.). New York, USA: Springer.

    MATH  Google Scholar 

  • Pal, N., C. Jin, and W. K. Lim 2006. Handbook of Exponential and Related Distributions for Engineers and Scientists. Boca Raton, FL, USA: Chapman & Hall/CRC.

    Google Scholar 

  • Prentice, R. L. 1974. A log gamma model and its maximum likelihood estimation. Biometrika 61(3):539–544.

    Article  MATH  MathSciNet  Google Scholar 

  • Richards, S. J. 2012. A handbook of parametric survival models for actuarial use. Scandinavian Actuarial Journal 2012(4):233–257.

    Article  MATH  MathSciNet  Google Scholar 

  • Rinne, H. 2009. The Weibull Distribution. Boca Raton, FL, USA: CRC Press.

    Google Scholar 

  • Schepsmeier, U. and J. Stöber 2014. Derivatives and Fisher information of bivariate copulas. Statistical Papers 55(2):525–542.

    Article  MATH  MathSciNet  Google Scholar 

  • Shao, J. 2005. Mathematical Statistics: Exercises and Solutions. New York, USA: Springer.

    Google Scholar 

  • Stacy, E. W. 1962. A generalization of the gamma distribution. Annals of Mathematical Statistics 33(3):1187–1192.

    Article  MATH  MathSciNet  Google Scholar 

  • Titterington, D. M., A. F. M. Smith, and U. E. Makov 1985. Statistical Analysis of Finite Mixture Distributions. New York, USA: Wiley.

    MATH  Google Scholar 

  • Trivedi, P. K. and D. M. Zimmer 2005. Copula modeling: An introduction for practitioners. Foundations and Trends in Econometrics 1(1):1–111.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Auckland, Auckland, New Zealand

    Thomas W. Yee

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  1. Thomas W. Yee
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Yee, T.W. (2015). Univariate Continuous Distributions. In: Vector Generalized Linear and Additive Models. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2818-7_12

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