Three yearly losses.
Second & Third: Weibull
Losses are independent.
Find the 95% VaR of the min loss
The Attempt at a Solution
My first thought was:
Let L be total loss, A be first Loss, B be second loss, C be third loss
Pr(L<x) = Pr(A<x) * Pr(B<x) * Pr(C<x)
But logically this seems wrong to me, because if Pr(A<x) = 100% then Pr(L<x) should be 100%.
So then I thought maybe:
Pr(L<x) = a_1 Pr(A<x) + a_2 Pr(B<x) + a_3 Pr(C<x)
but how do I choose a_1, a_2,a_3? Seems like these would change based on the values of A,B,C which makes them r.v. themselves!
The prof hinted that we just need to find the CDF and that to find the CDF we first should find the survival function keeping in mind the r.v. are independent.
I'm sort of out of ideas.