Now I need a (maybe approximated) model for this distribution:
$$X=(x_1, x_2, …, x_n)$$ where $x_i$ is a real number between $0.0$ and $1.0$, and the sum of $x_i$ equals $1.0$.
Now, I want to use Multivariate Normal Distribution to model this distribution. But the problem is that the values of the variables in Multivariate Normal Distribution are not constrained within $[0.0, 1.0]$, while in my practical distribution, $x_i$ is constrained within $[0.0, 1.0]$. In another word, the Multivariate Normal Distribution exceeds the feasible values in my practical distribution. As a result, the total area (or probability) under the possible part of the Normal distribution is less than $1$.
It's so strange! Can any one help me? Maybe I should use another distribution to approximate it?
Thanks a lot!
If you know that X is a bounded random variable, maybe you should use a different distribution to model it. I can't say which distribution without further information, but if it needs to be somewhat gaussian, you could use a truncated normal distribution (just an exemple). You could also use a normal distribution with low variance so that the probability to exceed $[0,1]$ is very low, but once again it depends on your data.