IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v14y2012i3d10.1007_s11009-012-9277-8.html
   My bibliography  Save this article

Extended Truncated Tweedie-Poisson Model

Author

Listed:
  • Jordi Valero

    (Technical University of Catalonia)

  • Josep Ginebra

    (Universitat Politècnica de Catalunya
    Technical University of Catalonia)

  • Marta Pérez-Casany

    (Technical University of Catalonia)

Abstract

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed Poisson distributions and that, other than under the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Extending the model also allows one to use the maximum likelihood based inference tools when the m.l.e. does not exist under the unextended model. The extended model is proved useful in the analysis of frequency count data.

Suggested Citation

  • Jordi Valero & Josep Ginebra & Marta Pérez-Casany, 2012. "Extended Truncated Tweedie-Poisson Model," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 811-829, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-012-9277-8
    DOI: 10.1007/s11009-012-9277-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-012-9277-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-012-9277-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dankmar Böhning & Ronny Kuhnert, 2006. "Equivalence of Truncated Count Mixture Distributions and Mixtures of Truncated Count Distributions," Biometrics, The International Biometric Society, vol. 62(4), pages 1207-1215, December.
    2. Willmot, Gordon E., 1988. "A remark on the poisson-pascal and some other contagious distributions," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 217-220, December.
    3. Xavier Puig & Josep Ginebra & Marti Font, 2010. "The Sichel model and the mixing and truncation order," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1585-1603.
    4. Ginebra, Josep & Puig, Xavier, 2010. "On the measure and the estimation of evenness and diversity," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2187-2201, September.
    5. D. I. Holmes, 1992. "A Stylometric Analysis of Mormon Scripture and Related Texts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 155(1), pages 91-120, January.
    6. Alex Riba & Josep Ginebra, 2006. "Diversity of vocabulary and homogeneity of literary style," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 729-741.
    7. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    8. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xavier Puig & Josep Ginebra & Marti Font, 2010. "The Sichel model and the mixing and truncation order," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1585-1603.
    2. Ginebra, Josep & Puig, Xavier, 2010. "On the measure and the estimation of evenness and diversity," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2187-2201, September.
    3. Venegas-Martínez, Francisco & Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo, 2015. "Riesgo operativo en el sector salud en Colombia: 2013," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(43), pages 7-36, segundo s.
    4. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    5. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    6. Eric Ghysels & Christian Gouriéroux & Joann Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO.
    7. Nabil Kazi-Tani, 2020. "Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria," Working Papers hal-01742638, HAL.
    8. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 374-381, December.
    9. P. Del Moral & G. W. Peters & Ch. Verg'e, 2012. "An introduction to particle integration methods: with applications to risk and insurance," Papers 1210.3851, arXiv.org, revised Oct 2012.
    10. Bae, Taehan & Kim, Changki & Kulperger, Reginald J., 2009. "Securitization of motor insurance loss rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 48-58, February.
    11. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    12. Emilio Gómez-Déniz & Jorge V. Pérez-Rodríguez & Simón Sosvilla-Rivero, 2022. "Analyzing How the Social Security Reserve Fund in Spain Affects the Sustainability of the Pension System," Risks, MDPI, vol. 10(6), pages 1-17, June.
    13. Willmot, Gordon E., 1997. "Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 25-42, October.
    14. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
    15. Alexandre Kurth & Dirk Tasche, 2002. "Credit Risk Contributions to Value-at-Risk and Expected Shortfall," Papers cond-mat/0207750, arXiv.org, revised Nov 2002.
    16. Franck Adékambi, 2019. "Moments Of Phase-Type Aging Modeling For Health Dependent Costs," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 37-64, June.
    17. Papalamprou, Konstantinos & Antoniou, Paschalis, 2019. "Estimation of capital requirements in downturn conditions via the CBV model: Evidence from the Greek banking sector," Operations Research Perspectives, Elsevier, vol. 6(C).
    18. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, October.
    19. Schlottmann, Frank & Seese, Detlef, 2004. "A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 373-399, September.
    20. Yuki Itoh, 2009. "Recovery Process Model for Two Companies," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 287-331, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-012-9277-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.