IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i7p2363-2371.html

Quasi-negative binomial distribution: Properties and applications

Author

Listed:
  • Li, Shubiao
  • Yang, Fang
  • Famoye, Felix
  • Lee, Carl
  • Black, Dennis

Abstract

In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting distribution of QNBD is the generalized Poisson distribution under certain conditions. A zero-inflated QNBD is also defined. Applications of QNBD and zero-inflated QNBD in various fields are presented and compared with some other existing distributions including Poisson, generalized Poisson and negative binomial distributions as well as their zero-inflated versions. In general, the QNBD or its zero-inflated version performs better than the other models based on the chi-square statistic and the Akaike Information Criterion, especially for the cases where the data are highly skewed, have heavy tails or excessive numbers of zeros.

Suggested Citation

  • Li, Shubiao & Yang, Fang & Famoye, Felix & Lee, Carl & Black, Dennis, 2011. "Quasi-negative binomial distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2363-2371, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2363-2371
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(11)00048-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. P.C. Consul & F. Famoye, 1986. "On The Unimodality Of Generalized Poisson Distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(2), pages 117-122, June.
    2. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    3. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
    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. Jamiu S. Olumoh & Osho O. Ajayi & Sauta S. AbdulKadir, 2022. "A quasi-negative binomial regression with an application to medical care data," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(5), pages 3029-3052, October.
    2. Mohanan Monisha & Damodaran Santhamani Shibu, 2024. "On Discrete Mixture of Moment Exponential Using Lagrangian Probability Model: Properties and Applications in Count Data with Excess Zeros," Annals of Data Science, Springer, vol. 11(6), pages 2035-2057, December.
    3. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.

    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. Brown, Sarah & Greene, William H. & Harris, Mark N. & Taylor, Karl, 2015. "An inverse hyperbolic sine heteroskedastic latent class panel tobit model: An application to modelling charitable donations," Economic Modelling, Elsevier, vol. 50(C), pages 228-236.
    2. Raslan Alzuabi & Sarah Brown & Mark N. Harris & Karl Taylor, 2024. "Modelling the composition of household portfolios: A latent class approach," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 57(1), pages 243-275, February.
    3. Jinli Duan & Feng Jiao & Qishan Zhang & Zhibin Lin, 2017. "Predicting Urban Medical Services Demand in China: An Improved Grey Markov Chain Model by Taylor Approximation," IJERPH, MDPI, vol. 14(8), pages 1-12, August.
    4. Bowker, James Michael & Starbuck, C. Meghan & English, Donald B.K. & Bergstrom, John C. & Rosenberger, Randall S. & McCollum, Daniel W., 2009. "Estimating the Net Economic Value of National Forest Recreation: An Application of the National Visitor Use Monitoring Database," Faculty Series 59603, University of Georgia, Department of Agricultural and Applied Economics.
    5. Alice Sanwald & Engelbert Theurl, 2017. "Out-of-pocket expenditures for pharmaceuticals: lessons from the Austrian household budget survey," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 18(4), pages 435-447, May.
    6. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    7. Erik Schokkaert & Tom Van Ourti & Diana De Graeve & Ann Lecluyse & Carine Van de Voorde, 2010. "Supplemental health insurance and equality of access in Belgium," Health Economics, John Wiley & Sons, Ltd., vol. 19(4), pages 377-395, April.
    8. 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, Universität Innsbruck.
    9. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    10. Hsin‐Fan Chen & Sheng‐Hung Chen & Jie‐Min Lee & Huei‐Yann Jeng, 2010. "Who Are the Potential Smokers of Smuggled Cigarettes?," Asian Economic Journal, East Asian Economic Association, vol. 24(3), pages 221-234, September.
    11. Galina Besstremyannaya & Richard Dasher & Egor Ganaga, 2024. "Consumer heterogeneity and the use of cashless payments in Japan in 2007–2020: a latent class approach," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 75, pages 33-53.
    12. Anikó Bíró, 2014. "Supplementary private health insurance and health care utilization of people aged 50+," Empirical Economics, Springer, vol. 46(2), pages 501-524, March.
    13. Zhou, Yang & Shi, Zhixiong & Shi, Zhengyu & Gao, Qing & Wu, Libo, 2019. "Disaggregating power consumption of commercial buildings based on the finite mixture model," Applied Energy, Elsevier, vol. 243(C), pages 35-46.
    14. Ziebarth, Nicolas R., 2013. "Long-term absenteeism and moral hazard—Evidence from a natural experiment," Labour Economics, Elsevier, vol. 24(C), pages 277-292.
    15. Gregory, Christian & Deb, Partha, "undated". "Who Benefits Most from SNAP?," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 236648, Agricultural and Applied Economics Association.
    16. Islam, Nizamul & Liégeois, Philippe & Berger, Frederic, 2010. "Discrete choice modelling of labour supply in Luxembourg through EUROMOD microsimulation," EUROMOD Working Papers EM5/10, EUROMOD at the Institute for Social and Economic Research.
    17. Deb, Partha & Trivedi, Pravin K., 2002. "The structure of demand for health care: latent class versus two-part models," Journal of Health Economics, Elsevier, vol. 21(4), pages 601-625, July.
    18. Deb, Partha & Gallo, William T. & Ayyagari, Padmaja & Fletcher, Jason M. & Sindelar, Jody L., 2011. "The effect of job loss on overweight and drinking," Journal of Health Economics, Elsevier, vol. 30(2), pages 317-327, March.
    19. Lee, Woojoo & Kim, Jeonghwan & Ahn, Jae Youn, 2020. "The Poisson random effect model for experience ratemaking: Limitations and alternative solutions," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 26-36.
    20. Partha Deb & Chenghui Li & Pravin K. Trivedi & David M. Zimmer, 2006. "The effect of managed care on use of health care services: results from two contemporaneous household surveys," Health Economics, John Wiley & Sons, Ltd., vol. 15(7), pages 743-760, July.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    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:eee:csdana:v:55:y:2011:i:7:p:2363-2371. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.