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Thread: Force of mortality

  1. #1
    Actuary.com - Level I Poster
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    Force of mortality

    Hi, I am so confused, I need to calculate the force of mortality from a life table, but I am not sure about if the life table contains the force of mortality in one of the columns, I am using mortality tables from HMD (www.mortality.org).

    the estructure of these tables is like this

    Year

    Year or range of years (for both period & cohort data)
    Age

    Age group for n-year interval from exact age x to just before exact age x+n, where n=1, 4, 5, or ∞ (open age interval)
    m(x)

    Central death rate between ages x and x+n
    q(x)

    Probability of death between ages x and x+n
    a(x)

    Average length of survival between ages x and x+n for persons dying in the interval
    l(x)

    Number of survivors at exact age x, assuming l(0) = 100,000
    d(x)

    Number of deaths between ages x and x+n
    L(x)

    Number of person-years lived between ages x and x+n
    T(x)

    Number of person-years remaining after exact age x
    e(x)

    Life expectancy at exact age x (in years)

    Can you explain me a method in order to calculate the force of mortality or maybe mx is the force of mortality??

    thanks for your explanation

  2. #2
    Actuary.com - Level II Poster
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    First you have to choose an assumption to interpolate mortality. Searching for DeMoivre's law, linear assumption or Balducci on the Internet will give you a starting point. In the process of calculating force of mortality, you'll be using and/or transforming some of the columns in the life table.

    Hope this helps.

  3. #3
    Actuary.com - Level I Poster
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    Quote Originally Posted by Iņaki Viggers View Post
    First you have to choose an assumption to interpolate mortality. Searching for DeMoivre's law, linear assumption or Balducci on the Internet will give you a starting point. In the process of calculating force of mortality, you'll be using and/or transforming some of the columns in the life table.

    Hope this helps.
    Hi Iņaki, What you refers with "interpolate mortality"??
    I am not very clear with this, mortality is qx, px or what?


    maybe first calculate the survival function and then use the definition of force of mortality given as \mu(x)=-S'(x)/S(x),?

    the how I should calculate the derivative? itīs ok if I calculate numerically with finite differences something like S'(x)=S(x+1)-S(x)/x+1-x , I think that in this case the denominator will be always 1 because age is 1 2 3 4 5 6 ..... and the difference betwen x+1 and x always will be 1?
    It īs ok my idea?


    thanks in advance for your explanation

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