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Suppose $X_1, \dots, X_n$ are truncated standard normal variables, truncated so that $X_i \geq 0$ (that is, $X_i$ is drawn as a standard normal, conditional on $X_i \geq 0$)

Let $c_1, \dots, c_n$ be non-negative coefficients.

What does the distribution of $\sum_i c_i Y_i$ look like? Does it have, or approximately have, a standard distribution, such as a truncated normal distribution?


Original question:
Suppose $X_1, \dots, X_n$ are iid Normal random variables, with mean 0 and variances $\sigma_1, \dots, \sigma_n$.

Let $Y_i = \max(0,X_i)$. (So $Y_i$ is a truncated normal random variable).

What does the distribution of $\sum_i Y_i$ look like? Does it have, or approximately have, a standard distribution?

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    You edited the question, based on my answer, in such a way that makes my answer look irrelevant. This is a bad practice, because it wasted my effort. The accepted way was to leave the original question in place, probably at the bottom of the question.2012-07-25

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