An alternative to the method of maximum likelihood as a method for the estimation of the parameters of a distribution. Each moment of a distribution can be expressed as a function of the parameters of the distribution, and often this implies that the parameters can be expressed as simple functions of the moments. In such cases, replacing the moments with their sample estimates provides estimates of the population parameters.
For example, the two-parameter gamma distribution with probability density function proportional to xα−1e−x/β has its first moment, μ′1 (equal to the mean, μ), given by μ=αβ and its second central moment, μ2, given by μ2=αβ2. Solving these equations, we get α=μ2/μ2 and β=μ2/μ. The method of moments replaces the unknown quantities μ and μ2 with the corresponding sample quantities and so that, for example, the estimator of α is ᾶ given by
A method of solving field problems in which a self-consistent set of equations, usually in matrix form, is generated involving a set of unknown parameters, for example currents on a conducting surface, and a set of known excitations, for example voltage sources; the set of equations is solved through inversion of the matrix to derive the unknown parameters. The generation of these equations involves the sampling of the effects of the unknown parameters at a finite number of points within the problem, and weighting of these effects in order to satisfy a set of boundary conditions at these points: the weighting or moment of these effects leads to the name method of moments.
In the case of an unknown set of currents, the boundary condition sampled is usually that of zero tangential electric field on a conductor: at each point chosen to enforce this condition, an expression for the radiated field from the unknown currents on the whole structure is derived and set equal to any externally applied fields. When applied to all of the chosen points, this gives rise to the self-consistent matrix equation, which is then solved.
- condensed bed
- condensed-matter physics
- condenser
- condenser microphone
- condensin
- Condillac, Étienne Bonnot de (1715–80)
- conditional
- conditional assertion
- conditional autoregressive model
- conditional branch
- conditional choice
- conditional cost of living index
- conditional distribution
- conditional equation
- conditional excluded middle
- conditional expectation
- conditional independence
- conditional instability
- conditionality
- conditional jump
- conditional logic
- conditionally convergent
- conditional negation
- conditional non-contradiction
- conditional obligation