Force of mortality

In actuarial science, force of mortality represents the instantaneous rate of mortality at a certain age measured on an annualized basis. It is identical in concept to failure rate, also called hazard function, in reliability theory.

In a life table, we consider the probability of a person dying from age ("x") to ("x"+1), called "q_x". In the continuous case, we could also consider the conditional probability of a person, who attained age ("x"), dying from age ("x") to age ("x"+"Δx") as:

where F_X(x) is the distribution function of the continuous age-at-death random variable, X. If we let "Δx" tend to zero, we get a function for force of mortality, denoted as "μ(x)":

$mu,(x)=frac\{F\text{'}\_X(x)\}\{1-F\_X(x)\}$

Since f_X(x)=F'_X(x) is the probability density function of X, and s(x)=1-F_X(x) is the survival function, force of mortality can also be expressed variously as:

$mu,(x)=frac\{f\_X(x)\}\{1-F\_X(x)\}=-frac\{s\text{'}(x)\}\{s(x)\}=-\{frac\{d\}\{dxln\; [s(x)]$

See also

* Failure rate
* Hazard function
* Actuarial present value
* Actuarial science
* Reliability theory

External links

*http://www.fenews.com/fen46/topics_act_analysis/topics-act-analysis.htm