No. 1028

Title:

(originally in Japanese) �¢‘Ñ�”‚Ì•Ï‘J

Author(s):

UEDA, Sumie (The Institute of Statistical Mathematics);
MAEHARA, Hiroshi (Ryukyu University)

Key words:

Household-size distribution, Marriage-delivery model

Abstract:

    Suppose that each household consists of parents and their children. We assume the following simple "Marriage-delivery" model: At time t, a boy and a girl are chosen at random from all children as a couple, and at time t+1, they marry, have k new children with probability p(k), and they make a new household of size k+2, where k=0,1,2,3,4. Furthermore, we suppose that the birth rates of male and female are equal, the expected value of k is equal to 2, and no child dies and no parents die until their children are all married. Under these assumptions, we show that the distribution of household-size tends to a certain distribution given by simple fractional functions of p(k), k=0,1,2,3,4, as t tends to infinity.