My intuition tells me that although the sum of X1 and Y1 will not be exactly
a truncated normal, you will find that a truncated normal offers a good
approximation if both means are far from zero where the truncated part is
small. If you simulate this system, you will develop a better feeling for
it.
"H. J. Wang" wrote:
> Hi,
>
> Suppose X, Y are independent random variables with normal distributions.
> The means and variances are different. Assume X1 and Y1 are random
> variables with the probability distributions f(X | X>=0) and g(Y|Y>=0),
> respectively. That is, X1 and Y1 the non-negative truncations of X and
> Y, respectively. Does anyone know whether in this case Z = X1 + Y1 is
> still a truncated normal? Any reference on this? Thanks in advance!
