Statistical inference with bivariate gamma distributions

In some experimental situations where the use of a covariate could increase the precision of the experiment the distributions of the test variate and the covariate are highly non-normal. Some of these cases can be analysed by using a bivariate Г distribution which is here defined. Methods of testing for a change in the scale parameter in one margin, using the other variate as a control, are described and the correponding extension to cross-over experiments briefly outlined.