Force of mortality

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 "qx". 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:

P(xx)=frac{F_X(x+Delta;x)-F_X(x)}{Delta;x(1-F_X(x))}

where FX(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'_X(x)}{1-F_X(x)}

Since fX(x)=F'X(x) is the probability density function of X, and s(x)=1-FX(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'(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


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