Notations used in Actuarial Tables

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arpit
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31 Jul 2018, 18:34

There are basically 4 notations -
  • lx: It is the number of surviving lives alive at exact age 𝑥.
  • 𝑑𝑥: It is the number of deaths over the year of age 𝑥.
  • qx: Probability of dying in year x
  • px: Probability of surviving year x
Now there are 4 relations that helps in understanding the tables-

1. l𝑥+1=𝑙𝑥−𝑑𝑥: It means the number of surviving person at age x+1 is equal to the number of surviving person at age x minus total deaths in year x

2. 𝑞𝑥=𝑑𝑥/𝑙𝑥: It means the number of deaths in a year divided by number of person living at age x

3. 𝑝𝑥=(𝑙𝑥+1)/lx: It means the probability of surviving  is equal to the number of people alive in year x +1 divided by the number of people died in the year x

4. px = 1-qx: It means that the probability of surviving is equal to 1 minus probability of death. In other words, the probability of surviving and probability of death equals 1


Collectively, 𝑙𝑥, 𝑑𝑥, 𝑞𝑥 and 𝑝𝑥 form what is called a “life table” or “actuarial table”.  

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