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2008 Dec 29
0
Lognormal with 0/1 "tag" [theoretical]
...tly distributed
with X is a "tag" Y: Y = 0 or 1, with
Prob(Y=1|X) = exp(L)/(1+exp(L)), L = a + b*X
I am interested in the distribution of X conditional on Y,
which is proportional to
f(x,Y) = dlnorm(x,mu,sigma)*exp(Y*L)/(1+exp(L))
(Y = 0 or 1, L = a + b*x)
In particular, before gettiong down to the computational work,
I am interested in studying its moments, and its "incomplete
moments":
Mj(X,Y) = Integral[x=0:X] x^j * f(x,Y) dx
What I'd like to find out (and the chances are that some people
on this list should know!) is what analytical forms may be
available for...