example of fundamental theorem of demography
Assume a population with a (age, sex, etc.) that is described by a vector , where represents the number of individuals in the population who possess the characteristic at a level , at time .
For example, consider age-groups, and assume is the number of individuals in the population that are aged 0 to 1 year, is the number of individuals aged 1 to 2 years, etc.
Suppose that the transition from one class to another is described by a matrix . In the case of age-groups, this matrix will for example describe mortality in a given age-group. This matrix, in the case of non deterministic modelling, will define a Markov chain.
The fundamental theorem of demography then states that if the matrix satisfies the required properties, then the distribution vector converges to the eigenvector associated to the dominant eigenvalue, regardless of the behavior of the total population .
Hence, in the case of age-groups, the proportion of individuals aged, say, 1 to 2 years, tends to a fixed value, even if the total population increases.
|Title||example of fundamental theorem of demography|
|Date of creation||2013-03-22 14:15:59|
|Last modified on||2013-03-22 14:15:59|
|Last modified by||mathcam (2727)|