IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v36y1998i4p415-420.html
   My bibliography  Save this article

An alternative representation of Altham's multiplicative-binomial distribution

Author

Listed:
  • Lovison, G.

Abstract

Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.

Suggested Citation

  • Lovison, G., 1998. "An alternative representation of Altham's multiplicative-binomial distribution," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 415-420, January.
    • Handle: RePEc:eee:stapro:v:36:y:1998:i:4:p:415-420
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)00088-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    2. Patricia M. E. Altham, 1978. "Two Generalizations of the Binomial Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(2), pages 162-167, 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. Gianfranco Lovison, 2015. "A generalization of the Binomial distribution based on the dependence ratio," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 126-149, May.
    2. Dankmar Böhning, 2015. "Power series mixtures and the ratio plot with applications to zero-truncated count distribution modelling," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 201-216, August.

    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. Molenberghs, Geert & Declerck, Lieven & Aerts, Marc, 1998. "Misspecifying the likelihood for clustered binary data," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 327-349, January.
    2. Dittrich, R. & Hatzinger, R. & Katzenbeisser, W., 2002. "Modelling dependencies in paired comparison data: A log-linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 39-57, July.
    3. Kromidha, Endrit & Li, Matthew C., 2019. "Determinants of leadership in online social trading: A signaling theory perspective," Journal of Business Research, Elsevier, vol. 97(C), pages 184-197.
    4. Kim, Chul & Jun, Duk Bin & Park, Sungho, 2018. "Capturing flexible correlations in multiple-discrete choice outcomes using copulas," International Journal of Research in Marketing, Elsevier, vol. 35(1), pages 34-59.
    5. Richards, Timothy J. & Hamilton, Stephen F. & Yonezawa, Koichi, 2018. "Retail Market Power in a Shopping Basket Model of Supermarket Competition," Journal of Retailing, Elsevier, vol. 94(3), pages 328-342.
    6. Timothy Tyler Brown & Juan Pablo Atal, 2019. "How robust are reference pricing studies on outpatient medical procedures? Three different preprocessing techniques applied to difference‐in differences," Health Economics, John Wiley & Sons, Ltd., vol. 28(2), pages 280-298, February.
    7. L. Sun & M. K. Clayton, 2008. "Bayesian Analysis of Crossclassified Spatial Data with Autocorrelation," Biometrics, The International Biometric Society, vol. 64(1), pages 74-84, March.
    8. Francesco Bartolucci & Claudia Pigini, 2018. "Partial effects estimation for fixed-effects logit panel data models," Working Papers 431, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    9. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    10. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
    11. Francesco Bartolucci & Claudia Pigini, 2017. "Granger causality in dynamic binary short panel data models," Working Papers 421, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    12. Battey, H.S. & Cox, D.R., 2022. "Some aspects of non-standard multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. Keon Lee, Seong, 2005. "On generalized multivariate decision tree by using GEE," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1105-1119, June.
    14. Harald Hruschka, 2022. "Analyzing joint brand purchases by conditional restricted Boltzmann machines," Review of Managerial Science, Springer, vol. 16(4), pages 1117-1145, May.
    15. Ivy Jansen & Geert Molenberghs, 2008. "A flexible marginal modelling strategy for non‐monotone missing data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 347-373, April.
    16. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.
    17. Miranda, Alfonso & Trivedi, Pravin K., 2020. "Econometric Models of Fertility," IZA Discussion Papers 13357, Institute of Labor Economics (IZA).
    18. Lesaffre, Emmanuel & Molenberghs, Geert & Scheys, Ilse, 1997. "Prediction and classification when the diagnostic classes are related," Computational Statistics & Data Analysis, Elsevier, vol. 25(1), pages 67-90, July.
    19. Dittrich, Regina & Francis, Brian & Hatzinger, Reinhold & Katzenbeisser, Walter, 2006. "Modelling dependency in multivariate paired comparisons: A log-linear approach," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 197-209, September.
    20. Molenberghs, Geert & Kenward, Michael G., 2010. "Semi-parametric marginal models for hierarchical data and their corresponding full models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 585-597, February.

    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:stapro:v:36:y:1998:i:4:p:415-420. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.