Rapid parametric density estimation

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly maximum likelihood estimation (MLE). There will be discussed inexpensive density estimators, for example literally fitting polynomial to the sample, which coefficients are calculated from just averaging monomials over the sample (estimators of moments). Another discussed basic application is fitting distortion to some standard distribution like Gaussian. The estimated parameters are approaching the optimal values with error dropping like $1/\sqrt{n}$, where $n$ is the sample size.