Testing for outliers in the power-law growth parameters of sets of recurrent events data

The problem of testing for an outlying value of the parameter ββ is considered when the power-law model for the intensity function λ(t)=αβtβ−1λ(t)=αβtβ−1 is fitted separately to each of a set of repairable systems or other units with recurrent events data. Although an exact FF statistic can be used for testing whether any specified unit is an outlier with respect to its value of ββ, in general the degrees of freedom differ between units so transformation to the same distribution is necessary in order to find the extreme value for testing for an outlier in any unit. Two transformations of FF to standard normal are found to work well. Transformation to a completely specified distribution implies that the problems of masking and swamping do not arise in this problem. The power of one common outlier test is examined by simulation and the procedure is illustrated on a set of rainfall data.