Formal demography has yet to move beyond assuming that demographic rates are constant over time, an assumption that is both unrealistic and constraining. To generalize the fixed rate stable model to the changing rate dynamic model, this paper explores the mathematical regularities that underlie...

When fertility increases in a previously stable population, the new stable population will be younger than the old one, and the two age distributions will cross at the mean age of the populations.

What does tempo-adjusted period life expectancy measure? Taking a cohort perspective, I show that under conditions of constant linear mortality shifts the tempo-adjusted period indicator translates exactly to the cohort born e¤0 (t) years earlier. I discuss the implications of cohort...

A number of indices have been used in recent years to calculate lifespan variation, each with different underlying properties. Although these indices are assumed to be interchangeable, little research has been conducted to show under which conditions this assumption is appropriate, or how to...

This note provides some earlier history of the relationship given in FormalRelationships1, "Life left equals life lived in stationary populations," (Goldstein2009) and shows that while the expectation of life at the mean age of the population is close to the mean age, this is not exactly so.

Adult mortality decline was the driving force of life-expectancy increase in many developed countries in the second half of the twentieth century. In this paper we study one of the most widely used models to capture adult human mortality - the Gompertz proportional hazards model. In its standard...

The age-specific growth function of an observed population and the reproductive value function based on the population´s current vital rates determine the intrinsic rate of growth implied by those vital rates through the simple relationship given in equation (1). That equation establishes the...

The metastable model generalizes the stable population model by allowing net maternity to change exponentially over age and time. As a result, the metastable model generates an exponentially quadratic birth trajectory, which is characterized by a constant proportion of births by age of mother....

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Cohort measures, describing a lifetime random variable are easily and unambiguously obtained using standard tools. On the contrary, the lifetime random variable, and therefore life expectancy, for the period setting cannot be unambiguously defined without additional simplifying assumptions. For...