Re: Z = U(0,1)*N(0,1) + U(0,1)*N(0,1) + ... + U(0,1)*N(0,1) is distributed how?

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.

The distribution cannot be obtained in closed form;
there are ways of evaluating it numerically, none
too easy to carry out. If you know enough real and
complex analysis, and wish to go into them, email me.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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