Census age, death age, whats my age again?

Discussion in 'CT4' started by withoutapaddle, Mar 5, 2006.

  1. Death age - age last birthday
    P'(x,t) - no. of people aged x last birthday at time t

    Census age - age nearest birthday * 1st jan
    P(x,t) - no. of people aged x nearest birthday * 1 jan
    n.b. P(x,t-)=P(x+1,t) since age definition changes * 1 jan

    then P'(x,t) = 0.5[P(x,t) + P(x+1,t)] (a)
    assuming even distribution of birthdays over year & t's are * 1st jan

    now E(x,t) = intergral(0,1) of P'(x,t)
    ~0.5[P'(x,0)+P'(x,1)] (b)
    = 0.5[P'(x,0) +P'(x,1-)] (c)

    since cohort churn is evenly distributed thru year(i.e. assuming birthdays are too)

    but substituting (a) into (b) & (c) give different answers. So which one do you use? one is double counting?
     

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