# What changes to your central exposure to risk calculation when birthdays are not uniformly distributed?

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So say you rate interval is policy year interval for those classified x nearest on policy anniversary.

and you are now told that birthdays occur on average 1/6 years after the policy anniversary on which they were x nearest.

Normally the formula to calculating exposure is 1/2 ( Px(t) + Px(t+1) ) [assuming Px(t) is linear]

From what I think, it changes to 1/2 (Px(t) + Px-1(t+1))

May someone explain to me why I am right or wrong?

commented Apr 14, 2016 by (330 points)
Your answer doesn't seem correct. If birthdays occur on average $$\frac{1}{6}$$ years after the policy anniversary, this means that there will be more birthdays occurring near the start of the policy year than towards the end of the policy year. So if birthdays occur $$\frac{1}{6}$$  years after the policy anniversary, a significant proportion of lives aged x-1 nearest birthday(in actual life age terms) will be aged x nearest on the policy anniversary and a significant proportion of lives age x nearest birthday( in actual life age terms) will be aged x+1 nearest on the policy anniversary.