Fitting Bivariate Generalized Binomial Models of the Sarmanov Type

- Journal title : Korean Journal of Applied Statistics
- Volume 22, Issue 2, 2009, pp.271-280
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2009.22.2.271

Title & Authors

Fitting Bivariate Generalized Binomial Models of the Sarmanov Type

Lee, Joo-Yong; Kim, Kee-Young;

Lee, Joo-Yong; Kim, Kee-Young;

Abstract

For bivariate binomial data with both intra and inter-class correlation, Danaher and Hardie (2005) proposed a bivariate beta-binomial model. However, the model is limited to the situation where the intra-class correlation is strictly positive. Thus it might be seriously inadequate for data with a negative intra-class correlation. Several authors have considered generalized binomial distributions covering a wider range of intra-class correlation which could relax the possible model restrictions imposed. Among others there are the additive/multiplicative and the beta/extended beta binomial model. In this study, bivariate models of the Sarmanov (1966) type are formed by combining each of those univariate models to take care of the inter-class correlation, and are evaluated in terms of the goodness-of-fit. As a result, B-mB and B-ebB are fitted, successfully, to real data and that B-mB, which has a wider permissible range than B-ebB for the intra-class correlation is relatively preferred.

Keywords

Intra/Inter-class correlation;generalized binomial distributions;Sarmanov type of bivariate models;

Language

Korean

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