Law of Total Variance - Higher Moments

Higher Moments

A similar law for the third central moment μ3 says

\mu_3(Y)=\operatorname{E}(\mu_3(Y\mid X))+\mu_3(\operatorname{E}(Y\mid X)) +3\,\operatorname{cov}(\operatorname{E}(Y\mid X),\operatorname{var}(Y\mid X)).\,

For higher cumulants, a simple and elegant generalization exists. See law of total cumulance.

Read more about this topic:  Law Of Total Variance

Famous quotes containing the words higher and/or moments:

    “... peace is a militant thing ... any peace movement must have behind it a higher passion than the desire for war. No one can be a pacifist without being ready to fight for peace and die for peace.”
    —Mary Heaton Vorse (1874–1966)

    “Even the most subjected person has moments of rage and resentment so intense that they respond, they act against. There is an inner uprising that leads to rebellion, however short- lived. It may be only momentary but it takes place. That space within oneself where resistance is possible remains.”
    —bell hooks (b. c. 1955)