Cross-sectional data, such as Census statistics, enable the re-enactment of household lifecourse through the construction of the household composition matrix, a tabulation of persons in households by their age and by the age of their corresponding household-heads. Household lifecourse is represented in the household composition matrix somewhat analogously to survivorship in a life-table in demography. A measure of household lifecourse is the average household size, specific to age of household-head. Associated with the age-specific household size is the age-interval 0-4, which yields average number of children present in households, also by age of head. Trajectories of re-enacted household lifecourses for Phoenix and for the State of Arizona are depicted here to track the gamma probability density function. Through this relationship also the association between household size, children per household, and fertility emerges. To the extent that housing conditions or tenure impact average household size, or other aspects of household composition, fertility in particular is discerned as a housing-related demographic attribute of households. Household size and headship ratio, both specific to age of head, are here shown to be analytically related to the household composition matrix, their product yielding the age-specific headship coefficient. As a measure incorporating parameters of households and dwellers, thus also characterizing occupied dwelling units, the headship coefficient emerges as a demographic indicator of housing in a community.