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?