Probability density function of counts in a bin under a Poisson process of mean λ_T = 3.5 before and after applying the background reduction at a level of r = 2. Because of the background reduction, probabilities of counts larger than 0 and equal or below r are set to 0. Although the original mean number of counts is λ_T = 3.5, after the background reduction is applied zero count becomes the most probable observation. The expected value of the background-reduced distribution can be estimated analytically by This estimator is a special case of the general estimator defined in Eq. (A.4).