Skip to main content
Log in

Estimating a multivariate model with discrete Weibull margins

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

Recently, a proposal for simulating correlated discrete Weibull variables has been suggested, based on the Gaussian copula. Although the procedure is straightforward and allows the user to directly assign the desired pairwise correlations between the discrete margins (or simply assign the correlation matrix of the Gaussian copula), on the other hand the estimation process is more tricky. In this work, we describe and assess, with a special focus on the bivariate case, three techniques for the estimation of the model parameters; an application to real data is provided as well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arbous, A. G., and J. E. Kerrich. 1951. Accident statistics and the concept of accident proneness. Biometrics 7 (4):340–432.

    Article  Google Scholar 

  • Barbiero, A. 2015a. DiscreteWeibull: Discrete Weibull distributions (Type 1 and 3), R package version 1.1. https://doi.org/CRAN.R-project.org/package=DiscreteWeibull.

  • Barbiero, A. 2015b. Simulating correlated discrete Weibull variables: a proposal and an implementation in the R environment. In International Conference of Computational Methods in Science and Engineering 2015, AIP conference proceedings 1702, eds. T. E. Simos, Z. Kalogiratou, and T. Monovasilis, 190017.

  • Barbiero, A. 2016. A comparison of methods for estimating parameters of the type I discrete Weibull distribution. Statistics and Its Interface 9 (2): 203–212.

    Article  MathSciNet  Google Scholar 

  • Barbiero, A., and P. A. Ferrari. 2015a. GenOrd: Simulation of ordinal and discrete variables with given correlation matrix and marginal distributions, R package version 1.4.0. https://doi.org/CRAN.R-project.org/package=GenOrd.

  • Barbiero, A., and P. A. Ferrari. 2015b. Simulating correlated Poisson variables. Applied Stochastic Models in Business and Industry 31 (5):669–680.

    Article  MathSciNet  Google Scholar 

  • Cario, M. C., and B. L. Nelson. 1997. Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL.

  • Englehardt, J. D., and R. C. Li. 2011. The discrete Weibull distribution: An alternative for correlated counts with confirmation for microbial counts in water. Risk Analysis 31: 370–381.

    Article  Google Scholar 

  • Englehardt, J. D. 2015. Distributions of autocorrelated first-order kinetic outcomes: Illness severity. PLoS ONE 10 (6):e0129042.

    Article  Google Scholar 

  • Ferrari, P. A. and A. Barbiero. 2012. Simulating ordinal data. Multivariate Behavioral Research 47 (4): 566–589.

    Article  Google Scholar 

  • Genest, C., and J. Nešlehová. 2007. A primer on copulas for count data. Astin Bulletin 37 (2):475–515.

    Article  MathSciNet  Google Scholar 

  • Joe, H. 2005. Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis 94 (2):401–419.

    Article  MathSciNet  Google Scholar 

  • Kocherlakota, S., and K. Kocherlakota. 1992. Bivariate discrete distributions. New York, NY: Marcel Dekker.

    MATH  Google Scholar 

  • Nakagawa, T., and S. Osaki. 1975. The discrete Weibull distribution. IEEE Transactions on Reliability 24 (5):300–301.

    Article  Google Scholar 

  • Nikoloulopoulos, A. K. 2013. Copula-based models for multivariate discrete response data. In Copulae in mathematical and quantitative finance, Lecture notes in statistics, ed. P. Jaworski, F. Durante, and W. Härdle, vol. 213, 231–49. Berlin, Heidelberg, Germany: Springer.

    Chapter  Google Scholar 

  • Padgett, W. J., and J. D. Spurrier. 1985. Discrete failure models. IEEE Transactions on Reliability 34 (3):253–256.

    Article  Google Scholar 

  • R Core Team 2016. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://doi.org/www.R-project.org.

  • Stein, W. E., and R. Dattero. 1984. A new discrete Weibull distribution. IEEE Transactions on Reliability 33 (2):196–197.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alessandro Barbiero.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barbiero, A. Estimating a multivariate model with discrete Weibull margins. J Stat Theory Pract 11, 503–514 (2017). https://doi.org/10.1080/15598608.2017.1292483

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2017.1292483

Keywords

AMS Subject Classification

Navigation