Inconsistencies between q0 and 4q1 and a0 and 4a1

[peterdavjohnson]

The conversion from mx to qx is done using the assumption that mx is equal to a constant force of mortality in the age interval. This gives:

nqx = 1 - exp(-n*nMx)

This implies that the separation factor, nax, is:

nax = n + 1/nMx - n/nqx

However, the 1a0 and 4a1 are replaced by the Coale-Demeny (see p. 20 of Coale and Demeny, 1983) west formulas (here for males):
1a0 = 0.33 if q0 >= 0.100
= 0.045 + 2.875 * q0

This seems to have been transformed to make it a function of m0 as:

1a0 = 0.33 if 1m0 >= 0.107
= 0.045 + 2.684 * 1m0

This does not give the correct results. I am working on the revised formula. Should be ready tomorrow.