nmxTonqx: Convert Death Rates to Death Probabilities
In jschoeley/pash: Pace-Shape Analysis of Life-tables

Convert Death Rates to Death Probabilities

1	nmxTonqx(nmx, nax, nx, mode)

`nmx`	Mortality rate in age interval [x, x+nx).
`nax`	Subject-time alive in [x, x+n) for those who die in same interval.
`nx`	Width of age interval [x, x+n).
`mode`	Conversion formula. "chiang", "cfm", or "udd".

Chiangs formula for the nmx->nqx conversion is

nqx = nx*nmx / (1+(nx-nax)*nmx).

It may produce probabilities > 1 in cases where age groups are wide, hazards are high and the nax is approximated using the uniform distribution of deaths or the constant force of mortality assumption. Therefore in these cases we use other conversion formulas.

nqx = 1 - exp(-nmx*nx),

assuming a constant force of mortality within the age interval [x, x+n), and

nqx = 1 - (1-nmx / (1+0.5*nmx))^nx,

assuming a uniform distribution of deaths within the age interval [x, x+n).

jschoeley/pash documentation built on May 20, 2019, 2:07 a.m.