ZHANG Yan wrote:
>Suppose T1,T2...Tn are i.i.d. nonnegative random variable with pdf f(t).
>For two fixed positive value a and b, I have to compute the following
>probability, could you plz give some suggestins? Thanks.
>
>
>Pr(T1+T2+...Tn < a, T1<b,T2<b...Tn<b) =
>
P(sum(T_i) < a | max(T_i) < b) P{max(T_i) < b}
The latter factor is F(b)^n, where F is the cdf for the common
distribution.
For n large enough (and usually that is not very large), you might be
able to approximate the first factor using a normal approximation. Let
m = E[T_1 | T_1 < b] and v = Var(T_1 | T_1 < b). Then the first
factor is approximately Phi((a-n m) / sqrt(n v)), where Phi is the
cdf for the standard normal.
Or perhaps it is easy somehow to compute the n-fold convolution of the
conditional distribution?
--
Stephen J. Herschkorn [EMAIL PROTECTED]
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
