方差定義見(jiàn)“概率論與數(shù)理統(tǒng)計(jì)(浙大四版)”P109.
樣本方差的標(biāo)準(zhǔn)定義見(jiàn)“概率論與數(shù)理統(tǒng)計(jì)(浙大四版)”P145，注意是除以1/(n-1)不是1/n，盡管根據(jù)方差定義，感覺(jué)應(yīng)該是除以1/n。看std的matlab幫助：There are two common textbook definitions for the standard deviation s of a data vector X.一個(gè)是除以n，一個(gè)是除以n-1。
通過(guò)除以1/(n-1)能證明樣本方差是方差的無(wú)偏估計(jì)，見(jiàn)“概率論與數(shù)理統(tǒng)計(jì)(浙大四版)”P151公式(3.20)，Hanyang Peng曾經(jīng)給我推過(guò)這個(gè)證明，很easy。
matlab函數(shù)var，matlab2013a幫助說(shuō)明
var normalizes V by N– 1 if N > 1, where N isthe sample size. This is an unbiased estimator of the variance ofthe population from which X is drawn, as long as X consists of independent, identically distributed samples. For N =1, V is normalized by 1.
V = var(X,1) normalizesby N and produces the second moment of the sample about its mean. var(X,0) is equivalent to var(X).
second moment：二階矩