Chi-squared components for tests of fit and improved models for the grouped exponential distribution

We consider testing for an exponential distribution with unspecified rate parameter when it is only possible to observe the counts in groups with boundaries specified before sighting the data. On the basis of a size and power study we recommend that tests of fit for the exponential distribution be based on the Anderson–Darling statistic and the SW2SW2 statistic recommended by Gulati and Neus [(2001). Goodness-of-fit statistics for the exponential distribution when the data are grouped. In: Huber-Carol, C., Balakrishnan, N., Nikulin, M.S., Mesbah, M., (Eds.), Goodness-of-Fit Tests and Validity of Models. Birkhauser, Boston, pp. 113–123 (Chapter 9)]. We also suggest that inference based on one of these be complemented by examination of the components of the X2X2 statistic. We illustrate how to use these components to give improved models.