BOUNDED BIVARIATE DISTRIBUTIONS WITH NEARLY NORMAL MARGINALS

A number of examples of nonnormal bivariate distributions whose margin al distributions are normal have been described in the literature. Suc h examples can be extremely useful in classroom discussions of univari ate and bivariate normality. The present note introduces a new, practi cally motivated example involving maximum and minimum daily temperatur es, in which the marginal distributions appear to be normally distribu ted, whereas the bivariate distribution is not. Two differences exist compared to previous examples: (1) there is a practical motivation; (2 ) despite the apparent normality of the marginal distributions, it can be shown that such normality cannot really be valid, except in an unr ealistic special case. The example illustrates a number of additional points that would be of value in a classroom discussion of univariate and bivariate distributions.