ABSTRACT
The next section (10.2) is devoted to the question of determining when the peak (or maximum) on a series of maps becomes sufficiently high that an alarm is sounded. For example, peaks on maps of disease rates will, of course, fluctuate over time, and it is of interest to be able to determine if and when the peaks are getting higher, in comparison with some baseline norm for such peaks. The Gumbel distribution is used as a model for the statistical distribution of extreme values; this distribution does not require the underlying distributions of regional values to be either normal, known, or identical. Cumulative sum surveillance methods are used to monitor these Gumbel variates, and these methods can also be extended for use when monitoring smoothed regional values (where the quantity monitored is a weighted sum of values in the immediate geographical neighborhood). The methods are illustrated by using several cancer mortality datasets for the United States.
