Can't be done without knowledge of the joint distributions of
Y(t1), Y(t2),..., Y(t).
Jon Cryer
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Date: Wed, 19 Apr 2000 16:46:32 +0200
From: Thomas Peter Burg <[EMAIL PROTECTED]>
Organization: University of Illinois at Urbana-Champaign
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Subject: density of integral(RV(t)~f(t), 0..T, dt)
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Does anyone know if there's an answer to the following problem:
I'm given a function of time Y(t), with the property that all values of
Y are
random variables which are drawn from a time dependent distribution with
known time dependent density f(t). I.e. the probability that Y(t)>x is
Integral(f(t),-inf..x,dt):
d/dx P( Y(t) > x ) = f(t)
With these facts given, is there anything that can be said about the
distribution of
Integral(Y(tau), 0..t, dtau) ??
or its density function?
Is there a nice expression for that in terms of the known density f(t)
in
general?
or maybe with specific assumptions about f? (E.g. Gaussian with mean(t)
and
var(t))
I'd greatly appreciate answers to any of these questions or any
references
that might deal with this problem.
Thanks,
Thomas Burg
Dept. of Physics,
Swiss Federal Institute of Technology
[EMAIL PROTECTED]
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Department of Statistics http://www.stat.uiowa.edu\ \_ University
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