Multiple (Birth, Death)-processes and their applications to demographic problems
by
Kunasekaran Gopalakrishnan
Periyar University, India

Stochastic point process models are widely used in every domain of application where

a sequence of times - each time corresponding to the occurrence of some events -

constitute the observable data. Vital statistics are data on the occurrence of

fundamental events of human lives such as birth, death, marriage, and the like.

Brillinger discusses the demographic problems through the general properties

of point processes: The observation of Brillinger is that a Poisson property

of the population birth process enhances a two dimensional "Poissoness" of the

population death process. He argues that, assuming Poisson birth times and independent

life times, the number of deaths and the corresponding mid year population in an open

population have a bivariate Poisson distribution.

However both fertility and mortality rates differ, in general, between the two sexes.

It is un satisfactory in a stochastic model to have to ignore such a chance departure.

Thus it is more appropriate to represent the birth times by a bivariate point process

instead of a univariate point process such as Poisson process. In this paper, assuming

Poisson birth times and independent life times , it is shown that the death process is

a bivariate planar compound Poisson process.

Further, the concept of two dimensional vital rates has been introduced and their

joint probability distributions are obtained.

PDF

Date received: December 16, 2006