EFFECT OF BACKGROUND ON THE LEAST-SQUARES ESTIMATION OF EXPONENTIAL DECAY PARAMETERS

The effect of background on the statistical precision of exponential decay rates is examined using Monte Carlo calculations and direct evaluation of the least-squares error matrix. For typical observation time ranges, the presence of an unknown background reduces the precision in the decay rate by an order of magnitude. However, the uniform background is practically the worst case, and if the background distribution is ''shaped'' and if this shape can be ascertained independent of the decay data, the loss in precision can be greatly reduced. For the uniform background, the strong correlation between the decay parameter and the background parameter can be broken by operating at less than 100% duty cycle, such that the background is recorded independent of the signal some of the time. This approach can yield precision approaching that for the case of an a priori known background.