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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
3
votes
Bounding statistical distance by matching moments
Here's an article that is related to your question: How well do moments determine a distribution?
1
vote
Integral over error function and normal distribution
This looks like a Laplace approximation. If $\sigma^2$ is small, the integral of $f(x)$ times a normal density is essentially $f(\mu)$. You could see this by expanding $f(x)$ in a power series centere …