Perhaps best handled by the stats stack exchange but I would like a theoretical understanding as well as a suggestion and I reckon it's the same people on here as there anyway.
I want to know how to do a sensitivity analysis on 3 proportions $(a, b, c)$ where $a + b + c = 1$.
It is obvious to me that on 2 proportions, $(a, b)$, where $a + b = 1$ that I can jitter $a$ slightly and take $b$ as $1 - a$. This is because the variance of $a$ and $b$ are the same.
$Var(a) \approx a(1-a) = (1-b)b = b(1 - b) \approx Var(b)$.
But this doesn't work for 3 variables. For 1, if $a$ and $b$ are jittered enough then this forces $c$ to be negative which doesn't work for proportions.
How do I implement this computationally for $n$ proportions such that their sum is $1$? and Why?