Lost in translation
Actuaries have a long-standing habit of using different terminology to statisticians. This page lists some common terms used by actuaries in mortality work and their "translation" for a non-actuarial audience. The terms and notation are those used by actuaries in the UK, but in every country I have visited the local actuaries have used similar notation.
Table 1. Common actuarial terms and their definition for statisticians.
Actuarial term | Actuarial notation | Statistical description |
---|---|---|
central exposed to risk | \(E^c_x\) | The time exposed to risk of dying at age \(x\). |
curve of deaths | \({}_tp_x\mu_{x+t}\) | Probability density function for the future lifetime of an individual currently alive and aged exactly \(x\). |
force of mortality |
\(\mu_x\)
| In models with a single mortality decrement, this refers to the instantaneous hazard rate for mortality at exact age \(x\). In models with multiple states, this refers to the instantaneous transition intensity for mortality. |
initial exposed to risk | \(E_x\) | The number of individuals alive aged exactly \(x\) at the start of an investigation period. |
mortality law | varies | A functional form for the instantaneous hazard rate or probability of death, e.g. the Gompertz Law is \(\mu_x=\exp(\alpha+\beta x)\). |
mortality rate | \(q_x\) | The probability of death between ages \(x\) and \(x+1\) in a Bernoulli model for the number of deaths, given that a life is alive at exact age \(x\) at outset. |
survival rate | \({}_tp_x\) | The probability of survival from age \(x\) to age \(x+t\), given a life is alive at exact age \(x\), i.e. the survival curve or survivor function. |
It is interesting to note the different traditions within particular disciplines. For example, actuaries almost always use \(\mu_x\) to denote the force of mortality. Engineers, however, call the same thing the failure rate and typically denote it by \(\lambda\). Statisticians, meanwhile, will call the self-same concept the hazard function.
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A related translation table for non-statisticians can be found at Lost in Translation Reprise http://www.longevitas.co.uk/site/informationmatrix/lostintranslationrep…
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