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:

“A man should have a farm or a mechanical craft for his culture. We must have a basis for our higher accomplishments, our delicate entertainments of poetry and philosophy, in the work of our hands.”
—Ralph Waldo Emerson (1803–1882)

“The government does not concern me much, and I shall bestow the fewest possible thoughts on it. It is not many moments that I live under a government, even in this world. If a man is thought- free, fancy-free, imagination-free ... unwise rulers or reformers cannot fatally interrupt him.”
—Henry David Thoreau (1817–1862)