momentmetodens

Momentmetodens, or the method of moments, refers to a family of techniques that use moments of a distribution or function to infer parameters or to solve equations. In statistics, the method of moments estimates distribution parameters by equating the population moments (such as the mean and variance) with the corresponding sample moments. This yields simple algebraic estimators. Common examples include estimating a Poisson parameter by the sample mean, an exponential rate by the reciprocal of the sample mean, or a normal distribution by matching the first two moments. The method is straightforward and computationally light, but it can be less efficient than maximum likelihood estimation and may be biased in small samples or when higher-order moments are uninformative.

In computational mathematics and engineering, the method of moments is a numerical technique for solving integral equations, notably in electromagnetics. Unknown currents on conductors are expanded in basis functions and the integral equation is tested against a set of testing functions, producing a linear system that approximates the problem. The approach is flexible and capable of handling complex geometries and materials, and it is widely used in antenna design and scattering problems. Its performance depends on the choice of basis and testing functions and on discretization; dense system matrices and conditioning issues can pose practical challenges.

The term spans these and other domains, united by the core idea of solving problems through projections, moments, or projections onto a finite set of basis-like quantities.