# Method of moments (probability theory)

*34,190*pages on

this wiki

Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language |
Individual differences |
Personality |
Philosophy |
Social |

Methods |
Statistics |
Clinical |
Educational |
Industrial |
Professional items |
World psychology |

**Statistics:**
Scientific method ·
Research methods ·
Experimental design ·
Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

*See method of moments (statistics) for an account of a method of parameter estimation.*

In probability theory, the **method of moments** is a way of proving convergence in distribution by proving convergence of a sequence of moment sequences. Suppose *X* is a random variable and that all of the moments

exist. Further suppose the probability distribution of *X* is completely determined by its moments, i.e., there is no other probability distribution with the same sequence of moments
(cf. the problem of moments). If

for all values of *k*, then the sequence {*X*_{n}} converges to *X* in distribution.

The method of moments is especially useful for proving limits theorems for random matrices with independent entries, such as Wigner's semi-circle law.

This page uses Creative Commons Licensed content from Wikipedia (view authors). |