Bacon With Your Eggs? Applications of a New Bivariate Beta-Binomial Distribution

We present two everyday applications of a new bivariate beta-binomial distribution. Although the applications are familiar, they share unique characteristics that cannot be handled adequately by existing bivariate discrete distributions. These features are high levels of between- and within-trial co...

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Bibliographic Details
Published in:The American statistician 2005-11, Vol.59 (4), p.282-286
Main Authors: Danaher, Peter J, Hardie, Bruce G. S
Format: Article
Language:English
Subjects:
Beta-binomial
Binomial distribution
Binomial distributions
Binomials
Bivariate discrete distribution
Correlations
Distribution theory
Eggs
Exact sciences and technology
Marketing
Mathematics
Maximum likelihood estimation
Modeling
Multivariate analysis
Probability and statistics
Probability theory and stochastic processes
Random variables
Sarmanov distribution
Sciences and techniques of general use
Shopping trips
Statistical analysis
Statistical methods
Statistics
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Description
Summary:We present two everyday applications of a new bivariate beta-binomial distribution. Although the applications are familiar, they share unique characteristics that cannot be handled adequately by existing bivariate discrete distributions. These features are high levels of between- and within-trial correlation for the bivariate random variables. Our model is derived from a broad class of bivariate models based on a versatile, but little-known, family of distributions due to Sarmanov. For the applications presented, we show that our model fits observed data very well. In addition, for the bacon and eggs application, the model can be used to help improve the management of inventory in grocery stores.
ISSN:0003-1305
1537-2731
DOI:10.1198/000313005X70939