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Zero-Inflated, Zero-Altered and Positive Discrete Distributions

  • Thomas W. Yee
Part of the Springer Series in Statistics book series (SSS)

Abstract

This chapter looks at positive (0-truncated), zero-inflated and zero-altered (hurdle) distributions, with the focus on discrete distributions. Zero-deflated distributions are also mentioned. Specific examples include the zero-inflated Poisson and positive-binomial distributions. Another example concerns closed-population capture–recapture estimation, which is described in relatively more detail as an application of a positive-Bernoulli distribution. Reduced-rank variants of some of the above models are also considered.

Keywords

Wing Length Sampling Occasion Family Function Parent Distribution Deer Mouse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Amstrup, S. C., T. L. McDonald, and B. F. J. Manly 2005. Handbook of Capture–Recapture Analysis. Princeton: Princeton University Press.Google Scholar
  2. Baillargeon, S. and L.-P. Rivest 2007. Rcapture: Loglinear models for capture–recapture in R. Journal of Statistical Software 19(5):1–31.CrossRefGoogle Scholar
  3. Burnham, K. P. and D. R. Anderson 2002. Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach (Second ed.). New York: Springer.Google Scholar
  4. Cameron, A. C. and P. K. Trivedi 2013. Regression Analysis of Count Data (Second ed.). Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  5. Hilbe, J. M. 2011. Negative Binomial Regression (Second ed.). Cambridge, UK; New York, USA: Cambridge University Press.Google Scholar
  6. Horvitz, D. G. and D. J. Thompson 1952. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47(260):663–685.zbMATHMathSciNetCrossRefGoogle Scholar
  7. Huggins, R. and W.-H. Hwang 2011. A review of the use of conditional likelihood in capture–recapture experiments. International Statistical Review 79(3):385–400.zbMATHCrossRefGoogle Scholar
  8. Huggins, R. M. 1989. On the statistical analysis of capture experiments. Biometrika 76(1):133–140.zbMATHMathSciNetCrossRefGoogle Scholar
  9. Huggins, R. M. 1991. Some practical aspects of a conditional likelihood approach to capture experiments. Biometrics 47(2):725–732.CrossRefGoogle Scholar
  10. Hwang, W.-H. and R. Huggins 2011. A semiparametric model for a functional behavioural response to capture in capture–recapture experiments. Australian & New Zealand Journal of Statistics 53(4):403–421.MathSciNetCrossRefGoogle Scholar
  11. Johnson, N. L., A. W. Kemp, and S. Kotz 2005. Univariate Discrete Distributions (Third ed.). Hoboken, NJ, USA: John Wiley & Sons.zbMATHCrossRefGoogle Scholar
  12. Kleiber, C. and A. Zeileis 2008. Applied Econometrics with R. New York, USA: Springer.zbMATHCrossRefGoogle Scholar
  13. Liu, H. and K. S. Chan 2010. Introducing COZIGAM: An R package for unconstrained and constrained zero-inflated generalized additive model analysis. Journal of Statistical Software 35(11):1–26.CrossRefGoogle Scholar
  14. McCrea, R. S. and B. J. T. Morgan 2015. Analysis of Capture–Recapture Data. Boca Raton, FL, USA: Chapman & Hall/CRC.Google Scholar
  15. Otis, D. L., K. P. Burnham, G. C. White, and D. R. Anderson 1978. Statistical inference from capture data on closed animal populations. Wildlife Monographs 62:3–135.Google Scholar
  16. Tutz, G. 2012. Regression for Categorical Data. Cambridge: Cambridge University Press.Google Scholar
  17. Vuong, Q. H. 1989. Likelihood ratio tests for model selection and nonnested hypotheses. Econometrica 57(2):307–333.zbMATHMathSciNetCrossRefGoogle Scholar
  18. Webb, M. H., S. Wotherspoon, D. Stojanovic, R. Heinsohn, R. Cunningham, P. Bell, and A. Terauds 2014. Location matters: Using spatially explicit occupancy models to predict the distribution of the highly mobile, endangered swift parrot. Biological Conservation 176:99–108.CrossRefGoogle Scholar
  19. Welsh, A. H., R. B. Cunningham, C. F. Donnelly, and D. B. Lindenmayer 1996. Modelling the abundances of rare species: statistical models for counts with extra zeros. Ecological Modelling 88(1–3):297–308.CrossRefGoogle Scholar
  20. Welsh, A. H., D. B. Lindenmayer, and C. F. Donnelly 2013. Fitting and interpreting occupancy models. PLOS One 8(1):1–21.CrossRefGoogle Scholar
  21. Williams, B. K., J. D. Nichols, and M. J. Conroy 2002. Analysis and Management of Animal Populations. London: Academic Press.Google Scholar
  22. Winkelmann, R. 2008. Econometric Analysis of Count Data (5th ed.). Berlin: Springer.Google Scholar
  23. Winkelmann, R. and S. Boes 2006. Analysis of Microdata. Berlin: Springer.zbMATHGoogle Scholar
  24. Yang, H.-C. and A. Chao 2005. Modeling animals’ behavioral response by Markov chain models for capture–recapture experiments. Biometrics 61(4):1010–1017.zbMATHMathSciNetCrossRefGoogle Scholar
  25. Yee, T. W. 2014. Reduced-rank vector generalized linear models with two linear predictors. Computational Statistics & Data Analysis 71:889–902.MathSciNetCrossRefGoogle Scholar
  26. Yee, T. W., J. Stoklosa, and R. M. Huggins 2015. The VGAM package for capture–recapture data using the conditional likelihood. Journal of Statistical Software 65(5):1–33.CrossRefGoogle Scholar

Copyright information

© Thomas Yee 2015

Authors and Affiliations

  • Thomas W. Yee
    • 1
  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand

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