New classes of discrete bivariate distributions with application to football data

ABSTRACT

Motivated by Lee and Cha [The American Statistician 69 (2015) 221–230], we introduce 18 new families of discrete bivariate distributions. We give explicit expressions for their probability mass functions, cumulative distribution functions, product moments, and moment-generating functions. We reanalyze the football data in Lee and Cha (2015) and show that some of the newly proposed distributions provide better fits than the two families proposed by Lee and Cha.

KEYWORDS:

• Chisquare goodness-of-fit statistic
• Correlation
• Football data

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E99

Acknowledgments

The authors would like to thank the editor and the referee for careful reading and comments which greatly improved the article.