What is a quadravariate distribution? Question: What is a quadravariate distribution?
Motivation: I found a reference to quadravariate distributions in Priestley (1981) Spectral Analysis and Time Series on p325, but no definition (the author seems to think it is common knowledge). 10 minutes of googling revealed that the term gets used in quite a few papers, but I am still unable to find a definition anywhere.
 A: I'd interpret it to be a distribution on 4 variables - the next in the series univariate, bivariate, trivariate, .... 
It's a multivariate random variable with four components.
However, the word is more often spelled quadrivariate, which might explain why you had trouble finding it. 
To clarify; consider a gamma random variable $X\sim\text{gamma}(\alpha,\beta)$. That's univariate random variable; we say that the distribution of $X$ is a univariate distribution.
Now consider independent Poisson random variates $Z\sim\text{Pois}(\zeta)$, $X_1\sim\text{Pois}(\lambda_1)$ and $X_2\sim\text{Pois}(\lambda_2)$, and let $Y_1=X_1+Z$ and $Y_2=X_2+Z$. Then the distribution of $\left(\begin{array}{c}Y_1\\Y_2\end{array}\right)$ is an example of a bivariate Poisson distribution (in this case, one which has a correlation between its two components). Correspondingly $(Z,X_1,Y_2)'$ would be trivariate.
Now consider four independent normally distributed random variables $X_1,X_2,X_3$, and $X_4$, with mean vector $\mu=(\mu_1,\mu_1,\mu_1,\mu_0)'$ and variance-covariance matrix $\Sigma=\sigma^2I$. 
Then $\bf{X}$ $=(X_1,X_2,X_3,X_4)'$ is an example of a quadrivariate random variable.
So if for each observational unit I record four quantities, the observation on that unit is quadrivariate. The distribution of that quadrivariate random variable is a quadrivariate distribution.
