The effect of categorisation on testing for an exponential scale shift

A consequence of the fact that observations of random variables are discrete, is that the usual continuous models are inappropriate. Observations have an induced multinomial distribution where the cell probabilities depend on the form of the unobservable continuous distribution. We discuss one particular case: testing for the scale parameter of an exponential distribution. Sizes, powers and asymptotic relative efficiencies are used to assess the effect of categorisation. There are many parameters and we have not given a complete assessment. However our discussion gives a guide to the approach that may be adopted in similar cases. In the case we discuss, we give a preferred procedure that appears to be more convenient and less objectionable than its obvious competitors.