After a mathematical inspection of demographic models of kin frequencies, this article shows that lack of parity structure is the most problematic weakness of existing models. Since Lotka's age-structured population model ignores birth order, kin counts based on Lotka model inevitably assume Poisson distribution for parity. This assumption causes some discrepancies in kin models.
Effort is made to develop kin frequency model on age-parity-structured population model. Fertility rate by birth order is obtained from 1987 Japan National Fertility Survey, and female life table with parity structure is constructed. Intrinsic growth rate is calculated to get stable population model with parity. Expressions to attain various kin counts and family life cycle are developed and results are compared with those derived from Lotka model.
Based on age-parity life table, parity distribution at the end of reproductive ages shows smaller value of variance than means. This means that, unlikely the existing models predict, expected number of sisters is smaller than that of daughters when fertility is at or below replacement level. In the population before fertility transition, this relationship would reverse.
Comparison between stationary and stable population shows that relative number of first child falls when population has negative growth rate. Reduction in size of mothers' cohort causes this relationship.
Correct number of sisters or sibling is essential since it determines eventual number of various kin categories. Presumption of Poisson distribution would overestimate the number of indirect kin in population after fertility transition. It is inferred that fertility change results in greater change of the number of distant kin than close kin does. Numerical output supports this inference.