The heart of signature analysis is the Fisher information matrix which defines the information content in a group of observations. The observations are classified as known observables n1, n2..ni, each one with measured uncertainty sigma1, sigma2..sigmai (standard deviations). In order to define the information content, the observer relates the observables to a model he or she constructs with certain parameters, each parameter is defined as a known function of some or all of the observables. So that we have model parameters f1(n1, n2..ni), f2(n1, n2..ni)..fj(n1, n2..ni). The Fisher information matrix quantifies the information content of j x j elements, each element is the sum of partial derivatives over all the observables, generally expressed as inverse terms of the variances sigma12, sigma22..sigmai2.

The inverted Fisher matrix, also known as the co-variance matrix whose elements express the uncertainties of the observer’s model. Here, the co-variance matrix is simply the variances and co-variances of the age trend groups, each humor line has age trend profile which decides its membership to one of four groups; falling, rising, peaking or constant age trend. The co-variance elements are derived from the collective scores of the groups, the results presented herein will only show comparisons with the diagonal elements; the variances of the trend groups. The elements define in their totality the best possible estimators of the signatures of the data, also known as the Cramer-Rao Bound (CRB).

Signature analysis is applied to scaled humor appreciation scores from on-line surveys. The observables of the Fisher matrix are the average line scores of participants in all age groups, which define the age profile of lines of humor, therefore there are four signatures with their CRB’s.

The graphical representations show remarkable agreement between the age trend profiles of individual humor lines and group signatures. The agreement is most noticeable when the number of lines are highest (96 lines). It is immediately possible to see which line has typical and which has atypical age profile. And where typical values are identified then the proximity to meeting the CRB (best estimator limits) was systematic and strikingly small. Graphic results will show examples of profiles from the four trend groups and the group signatures and CRB’s. There is uniformity in the distribution of profile values; there are common offset values and the profiles are images of the signatures to a degree.

On plotting the distribution of offset compensated profile error with respect to signatures it becomes clear that age trending offers a valid typology for humor; the distributions will show convincing spikes close to the zero error, signifying matches are available between profiles and signatures in all trend groups.