Calculating force of mortality from life table The force of mortality at age $x+t$, given survival to $x+t$ is given by
$\mu_{x+t}$ $=-\frac{d}{dt}[ln({}_{t}p_{x})]$
Given a life table I know how to calculate ${}_{t}p_{x}$, but then how can I calculate the force of mortality using the formula above?  
 A: It's not 100% clear from your question what you need, but I'll mention some things that may help.
(Here $_tq_x$ is the probability a person alive at age $x$ will die by $x+t$, $q_x=\, _1q_x$ and $p_x=1-q_x$... unless I screwed up somewhere.)
$\mu_{x}$ is the force of mortality, i.e. the hazard rate.
$\mu_{x}=\lim_{t\to 0}\frac{_tq_x}{t} $
If you're working from a typical annual life table, one approximation may be found as follows:


*

*$p_x=\exp(-\int_0^1\mu_{x+t}dt)$  

*$\int_0^1\mu_{x+t}dt\approx \mu_{x+\frac12}$ (e.g. via a first order Taylor approximation at the center of the interval)


Hence $p_x\approx\exp(-\mu_{x+\frac12})$. Therefore:
$\mu_{x}\approx\frac12 (\mu_{x-\frac12}+\mu_{x+\frac12})$ (say via Taylor again)
$\qquad\approx -\frac12 (\log(p_{x-1})+\log(p_{x}))$ (using the above result),
though other approximations are also used; here are a couple:
$\mu_{x+t}\approx\frac{q_x}{1-tq_x}$ (uniform deaths)
$\mu_{x+t}\approx\frac{q_x}{1-(1-t)q_x}$ (Balducci assumption)
This last assumption can produce some odd results though.
You might also assume the table is locally well approximated by a Gompertz assumption (say) and approximate $\mu_{x+t}$ for small $t$ by taking values from the table at say $x$ and $x+1$ to work out the parameters near age $x$.
