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Multilingual Demographic Dictionary, second unified edition, English volume

Probability of dying

Multilingual Demographic Dictionary, second unified edition, English vol.
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Probability of dying  (PROBABILITY of dying)


Probabilities of dying 1 or death probabilities 1 are used to study in detail the mortality of a period or of a cohort. They are the probabilities that an individual of exact age x will die before exact age x + n, and are represented by the symbol nqx. If n = 1, we talk about annual death probabilities 2; if n = 5, about quinquennial death probabilities 3. The instantaneous death rate 4, or as it is occasionally called the force of mortality 4, is the limit of the nqx value as n tends to zero. The projective mortality probability 5★ is the probability that individuals of the same cohort or group of cohorts died between two January 1st. The name of this probability comes from its use in the calculation of population projections. It is also equal to 1-Lx+n/Lx, where Lx is the person-years lived by the stationary population from exact age x to exact age x+n. The complement to one of the probability of dying from exact age x to exact age x + n is the probability of survival 6 over this interval. In the preparation of population projections, we use survival ratios 7; they represent the probability that individuals of the same birth cohort or group of cohorts will still be alive n years later.

  • 1. The probability of death between age x and x + n is defined as the ratio of deaths between ages x and x+n to the number of survivors at exact age x. It is not to be confused with the central death rate, the ratio of deaths between ages x and x+n to the mean population alive at that age. The central death rate is written nmx .
  • 6. The probability of survival from age x to age x+n is written npx .
  • 7. A survival ratio is the complement to one of the projective mortality probability. Individuals in the cohorts do not have the same age and therefore are not at the same risk of dying.

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