- #1
Alexandra97
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I am looking for the solution of a multivariate gaussian integral over a vector x with an arbitrary vector a as upper limit and minus infinity as lower limit. The dimension of the vectors x and a are p $\times$ 1 and T is a positive definite symmetric p $\times$ p matrix. The integral is the following:
$$\int_{x=-\infty}^{x=a} x e^{ (-0.5 x'T^{-1}x)} d^p\bf{x}$$
I have tried to solve it with the cholesky decomposition and substitution with the Jacobian, but the dimension of the solution is not a p $\times$ 1 vector. When a equals $\infty$ the solution is of course an p $\times$ 1 vector of zero's (since it is the expected value).
Since I am not very experienced in integrating over vectors, also a good reference about this subject would be greatly appreciated.
$$\int_{x=-\infty}^{x=a} x e^{ (-0.5 x'T^{-1}x)} d^p\bf{x}$$
I have tried to solve it with the cholesky decomposition and substitution with the Jacobian, but the dimension of the solution is not a p $\times$ 1 vector. When a equals $\infty$ the solution is of course an p $\times$ 1 vector of zero's (since it is the expected value).
Since I am not very experienced in integrating over vectors, also a good reference about this subject would be greatly appreciated.