Among actuaries, force of mortality refers to what economists and other social scientists call the hazard rate and is construed as an instantaneous rate of mortality at a certain age measured on an annualized basis.
In a life table, we consider the probability of a person dying from age (x), that is, a person age x, to (x+1), a person age 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:
where FX(x) is the distribution function of the continuous age-at-death random variable, X. As Δx tends to zero, so does this probability in the continuous case. The approximate force of mortality is this probability divided by Δx. If we let Δx tend to zero, we get the function for force of mortality, denoted as μ(x):
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