The bivariate normal density with unit variance and correlation ρ is well known. We show that by integrating out ρ, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a uniform prior over ρ, then the marginal bivariate density depends...

Many statistical procedures assume that the underlying data-generating process involves Gaussian errors. Among the popular tests for normality, only the Kolmogorov--Smirnov test has a graphical representation. Alternative tests, such as the Shapiro--Wilk test, offer little insight as to how the...