Census data

Hi,

Can anyone please brief me how to adjust the definition of census data (Px,t to P'x,t) when it is different from the definition of death data (dx)?

a)dx = age last birthday Px,t = age nearest birthday
b)dx = age last birthday Px,t = age next birthday
c)dx = age nearest birthday Px,t = age last birthday
d)dx = age nearest birthday Px,t = age next birthday
e)dx = age next birthday Px,t = age last birthday
f)dx = age next birthday Px,t = age nearest birthday

copy and pasted from some1 forgot the name

 

here is P(x,t) to P'(x,t), to understand explanations draw age-interval at time 't'.

a)P'(x,t)=(P(x,t)+P(x+1,t))/2
Reason'(x,t) is the number of peoples at risk at exact age [x,x+1] having Age Last Birthday 'x' & but we have information of P(x,t) with Age Nearest Birthday 'x'. Age Nearest Birthday 'x' means exact age between [x-0.5,x+0.5]
we need age between [x,x+1] so we compare with [x-0.5,x+0.5](Age Nearest Birthday 'x') & [x+0.5,x+1.5](Age Nearest Birthday 'x+1').....
see [x,x+1]=[x,x+0.5]+[x+0.5,x+1]=[x-0.5,x+0.5]/2+[x+0.5,x+1.5]/2

age-interval for Age Next Birthday 'x' is [x-1,x]

try these...........
b)P'(x,t)=P(x+1,t)

c)P'(x,t)=(P(x-1,t)+P(x,t))/2

d)P'(x,t)=(P(x,t)+P(x+1,t))/2

e)P'(x,t)=P(x-1,t)

f)P'(x,t)=(P(x-1,t)+P(x,t))/2

 

Thanks Hermant you are a life saver, I can understand it using a timeline.

 

That's was a nice question! I posted my answer with pleasure!
BTW you'd s say age-line instead of timeline, because while equating number of lives at time 't' with different age definition, we consider same time 't' but different age-line.
Timeline is usable while calculating Lives Exposed to Risk.