Relations between demographic parameters

The mean life-expectancy e describes the average prospective life-time of an individual aged zero. This parameter can be explicitly described in terms of the survivorship distribution of the population. The Malthusian parameter r represents the asymptotic growth rate of a population. This parameter can be implicitly expressed in terms of the net-maternity distribution. The parameters e and r incompletely incorporate the age-specific fertility and mortality pattern of a population; distinct populations may have the same growth rate but different net-maternity functions; distinct populations may be characterized by the same mean life expectation but may have different survivorship distributions. This article analyzes a class of parameters called the entropy of a population (Demetrius, 1974a) which distinguishes between net-maternity functions with the same growth rate and also mortality distributions with the same mean life expectation. This class of parameters measures the convexity of the fertility and mortality distributions. This paper analyzes the relations between the entropy parameter and the standard demographic parameters.