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Computerization of the branching process
Author(s) -
Keyfitz Nathan,
Tyree Andrea
Publication year - 1967
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830120408
Subject(s) - iterated function , galton's problem , branching process , branching (polymer chemistry) , curiosity , extinction probability , dozen , genealogy , mathematics , exposition (narrative) , mathematical economics , combinatorics , sociology , arithmetic , psychology , history , demography , statistics , population , mathematical analysis , social psychology , materials science , literature , art , population size , composite material
The branching process had its origin in Galton's curiosity about the extinction of family names; the mathematics developed for this original purpose has since found many applications in physical as well as social science. The present paper gives an elementary summary of the theory in the iterated function first developed, and then translates this theory into matrix terms. The main substance of the exposition is the matrices which are produced by the computer, each power of which corresponds to an iteration of the function. The results, expressed in the original terms of Galton's question, show that each of us is very unlikely to have a few descendants, say a dozen generations hence; either our line will die out altogether, or else we will have hundreds of descendants. (This counts descendants of one sex only.) The probability of extinction of the female line is calculated as 0.8209 for the United States 1960; 0.4066 for Mexico 1960; 0.5142 for Israel 1961.