Sub-Poissonian and anti-bunching criteria via majorization of statistics

We use majorization and confidence intervals as a convenient tool to compare the uncertainty in photon number for different quantum light states. To this end majorization is formulated in terms of confidence intervals. As a suitable case study we apply this tool to sub- and super-Posissonian behavior and bunching and anti- bunching effects. We focus on the most significant classical and nonclassical states, such as Glauber coherent, thermal, photon number, and squeezed states. We show that majorization provides a more complete analysis that in some relevant situations contradicts the predictions of variance.