  This paper analyzes birth cohort effects and develops an approach which is
based on differential geometry to identify and measure cohort effects in
mortality data sets. The measurement is quantitative and provides a potential
method to compare cohort effects among different countries or groups. Data sets
of four countries (e.g. U.k., U.S., Canada and Japan) are taken as examples to
explain our approach and applications of the measurement to a modified
Lee-Carter model are analyzed. In fact, this paper is an upgrade version of our
paper arXiv:1504.00327. There is a new section which gives applications of our
approach based on the Lee-Carter and APC models.
