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Threshold studies in accounting use non-parametric methods to measure irregularities around the zero-earning threshold. More precisely, the discontinuity is measured by the difference between an observed population and a theoretical population locally estimated by interpolation of adjacent intervals. The sole hypothesis is that the distribution is assumed to be smooth in the absence of earnings management. The originality of this study lies in its identification of a mathematical earnings distribution function that can be used to parametrically measure the theoretical population (and irregularities). Such an approach allows the better measurement of discontinuities around thresholds, to better compare thresholds in space and over time, and to evaluate the amounts manipulated. The main empirical result of this study is the observation that although the numerous small-profit firms avoid losses, the amounts manipulated are not necessarily small. The study questions the postulate of “marginal manipulation” in earnings management to avoid thresholds.