At each age, tables such as table 1, provide 4 independent
ratios, , **i,j=1,2**. If we assume that the 4 unknown
forces are constant during , we may estimate these forces.
**T** is the interval between two rounds, i.e. about 2 years.

Matrix from equation 1 can be diagonalized; the eigenvalues are the roots of equation:

Since:

,
this equation leads to 2
distinct real and negative roots, and , **r>s**, where:

Therefore, , or the probability for an individual in
state **j** at time 0 to be in state k at time **t**, can be written:

Constants are determined by initial conditions at time 0:

and by conditions which derivates at time 0 must satisfy:

This leads to:

Since , the expression can also be written:

If corresponds to the () matrix with element , it can be written:

As is known from the LSOA survey for each single age, this leads to a system of four equations with four unknowns, , , and .

For the numeric calculations we used IMSL `dneqnf`

subroutine.
As **T** is about 2 years, we can either use single age or double age
(**x, x+2**) estimates.

Tue Jun 6 00:15:46 DF 1995