“method of moments”的概念、定义、翻译、参考文献-科学参考

method of moments

Statistics

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 x^α−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 $method of moments$

Electronics and Electrical Engineering

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.

单词	method of moments
释义	method of moments Statistics 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 x^α−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 $method of moments$ Electronics and Electrical Engineering 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.
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