  Nonclassicality criteria based on intensity moments and derived from the
usual matrix approach are compared to those provided by the majorization
theory. The majorization theory is shown to give a greater number of more
suitable nonclassicality criteria. Fifteen experimentally useful criteria of
the majorization theory containing the intensity moments up to the fifth order
are identified. Their performance is experimentally demonstrated on the set of
eleven potentially nonclassical states generated from a twin beam by
postselection based on detecting a given number of photocounts in one arm by
using an iCCD camera.
