Extrapolation of Threshold-Limited Null Measurement Frequencies

The total measurable level of a pathogen is due to many sources, which produce a variety of pulses, overlapping in time, that rise suddenly and then decay. What is measured is the level of the total contribution of the sources at a given time. But since we are only capable of measuring the total level above some threshold x0, we would like to predict the distribution below this level. Our principal model assumption is that of the asymptotic exponential decay of all pulses. We show that this implies a power law distribution for the frequencies of low amplitude observations. As a consequence, there is a simple extrapolation procedure for carrying the data to the region below x0.