Re: Z = U(0,1)*N(0,1) + U(0,1)*N(0,1) + ... + U(0,1)*N(0,1) is distributed how?
- From: "Stephen J. Herschkorn" <sjherschko@xxxxxxxxxxxx>
- Date: Fri, 13 Oct 2006 13:55:39 -0400
Herman Rubin wrote:
In article <1160685518.913251.102180@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
liam_herron <liam_herron@xxxxxxxxxxx> wrote:
If I have a r.v. Z which is the sum of n products where each product
is a Uniform r.v. multiplied by a standard normal r.v., what is the
distribution of Z? I am curious as I am simulating a factor loaded
model with random numbers.
I can reduce the cost of your simulation by half, as
Z is distributed as sqrt(\sum U_k^2)*W, where U_k are
independent uniform random variables, and W is normal.
Very nice!
Note that U^2 has a beta distribution. If I recall an investigation I once did correctly, you can often approximate the mixutre of beta distributions by a beta distribution. I don't know if the same applies to averages of betas, but if such an approximation will suffice for your simulation, you might check it out. If it works, you can replace the sum by a scaled beta.
--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan
.
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