A Simple Pile-up Model for Time Series Analysis

In this paper, a simple pile-up model is presented. This model calculates the probability P(n| N) of having n counts if N particles collide with a sensor during an exposure time. Through some approximations, an analytic expression depending on only one parameter is obtained. This parameter characterizes the pile-up magnitude, and depends on features of the instrument and the source. The statistical model obtained permits the determination of probability distributions of measured counts from the probability distributions of incoming particles, which is valuable for time series analysis. Applicability limits are discussed, and an example of the improvement that can be achieved in the statistical analysis considering the proposed pile-up model is shown by analyzing real data.