The Markovian binary tree applied to demography

We apply matrix analytic methods and branching processes theory to a comparison of female populations in different countries. We show how the same mathematical model allows us to determine characteristics about individual women, such as the distribution of her lifetime, the time until her first and her last daughter, and the number of daughters, as well as to analyze properties of the whole female family generated by a first woman, such as the extinction probability of the family, the distributions of the time until extinction, of the family size at any given time and of the total progeny.

[1]  Ronald Lee,et al.  Probabilistic Approaches to Population Forecasting , 1998 .

[2]  Jan M. Hoem,et al.  The Statistical Theory of Demographic Rates A Review of Current Developments , 1976 .

[3]  Nigel G. Bean,et al.  Markovian trees: properties and algorithms , 2008, Ann. Oper. Res..

[4]  Guy Latouche,et al.  Algorithmic Approach to the Extinction Probability of Branching Processes , 2011 .

[5]  Peter G. Taylor,et al.  Transient Markov arrival processes , 2003 .

[6]  Xiaoming Liu,et al.  Markov Aging Process and Phase-Type Law of Mortality , 2007 .

[7]  Ward Whitt,et al.  Squeezing the Most Out of ATM , 1995, IEEE Trans. Commun..

[8]  J. Scott Armstrong,et al.  Principles of forecasting , 2001 .

[9]  Cgb Mitchell,et al.  A REVIEW OF CURRENT DEVELOPMENTS , 1974 .

[10]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[11]  Guy Latouche,et al.  Transient features for Markovian binary trees , 2009, VALUETOOLS.

[12]  Florin Avram,et al.  Erlangian Approximations for Finite-Horizon Ruin Probabilities , 2002, ASTIN Bulletin.

[13]  Heather Booth,et al.  Demographic forecasting: 1980 to 2005 in review , 2006 .

[14]  Nico Keilman,et al.  Why population forecasts should be probabilistic - illustrated by the case of Norway , 2002 .

[15]  Guy Latouche,et al.  Newton's iteration for the extinction probability of a Markovian binary tree , 2008 .

[16]  S. Asmussen,et al.  Marked point processes as limits of Markovian arrival streams , 1993 .

[17]  P. Holgate,et al.  Matrix Population Models. , 1990 .

[18]  Douglas G. Woolford,et al.  Erlangized Fluid Queues with Application To Uncontrolled Fire Perimeter , 2005 .