2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223983Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a physically compelling interpretation of representing the highest precision with which the first cumulant of the random variable, i.e., its mean, can be estimated from its statistical realizations. We construct a complete hierarchy of information measures that determine the best precision with which all of the cumulants of a random variable -- and thus its complete probability distribution -- can be estimated from its statistical realizations. Several properties of these information measures and their generating functions are discussed.REVTeX v4, 8 pages; content revised, condensed; previous version: REVTeX v4, 15 pagesData Analysis, Statistics and Probabilitytext