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An asymmetry statistic of physical interest is an estimate of the ratio of the difference and the sum of the Poisson rate parameters for two scattering processes. Typically, an additive background signal contributes to measurements of each signal. Background is measured in a third experiment. Data are corrected by subtracting measured background. When the measured background is larger than one of the other measurements, background-corrected counts are negative. For this case, it would seem that no useful information can be extracted from the experiment. Here, asymmetry and an associated uncertainty interval are estimated for such cases using a bootstrap approach. [ABSTRACT FROM AUTHOR]

In many scattering experiments, the quantity of most direct physical interest is a measure of the difference between two closely related scattering signals, each generated by a Poisson scattering process. This difference is often expressed in terms of an asymmetry statistic, that is, the difference normalized to the sum of the two signals, corrected for an additive background contribution. Typically, a propagation of errors approach is used to compute confidence intervals for asymmetry. However, these confidence intervals are not reliable in general. In this work, generally accurate confidence intervals for asymmetry are obtained using a parametric bootstrap approach. Based on the observed data, data are simulated using a Monte Carlo resampling scheme. The resampled data sets satisfy a constraint that ensures that background-corrected count rates are not negative. [ABSTRACT FROM AUTHOR]