在Matlab中使用var求样本方差,使用std求标准差!
首先来了解一下方差公式:
p = [-0.92 0.73 -0.47 0.74 0.29; -0.08 0.86 -0.67 -0.52 0.93]p =
-0.9200 0.7300 -0.4700 0.7400 0.2900
-0.0800 0.8600 -0.6700 -0.5200 0.9300
var(p(1,:))ans =
0.5511
var(p(1,:),0)
ans =
0.5511
sum((p(1,:)-mean(p(1,:))).^2)/(length(p(1,:))-1)ans =
0.5511
上面三个结果相等,注意这里求的是样本方差,分母为n-1(样本数-1)。这是因为var函数实际上求的并不是方差,而是误差理论中“有限次测量数据的标准偏差的估计值。
var(p(1,:),1)ans =
0.4409
sum((p(1,:)-mean(p(1,:))).^2)/(length(p(1,:)))ans =
0.4409
上面两个结果求的才是母体方差,分母为n(样本数)
var没有求矩阵的方差功能,可使用std先求均方差,再平方得到方差。
std,均方差,std(p,0,1)求列向量方差,std(p,0,2)求行向量方差。
std(p(1,:))ans =
0.7424
sqrt(var(p(1,:)))ans =
0.7424
std(p,0,2)ans =
0.7424 %std(p(1,:))
0.7543 %std(p(2,:))
std(p,0,1)ans =
0.5940 0.0919 0.1414 0.8910 0.4525
若要求整个矩阵所有元素的均方差,则要使用std2函数:
std2(p)ans =
0.7058
协方差矩阵
A=[61.45,55.9,61.95,59,58.14,53.61,55.48,54.21,61.52,54.92];
B=[40.36,39.8,49.2,48,51.5,49.39,51.13,58.06,61,62.35];
C=[8.61,8.91,10.43,13.32,13.48,15.75,18.14,19.95,21.95,23.53];
D=[14.31,14.72,15.28,15.91,14.67,15,15.86,15.16,13.72,12.94];
E=[7.67,7.75,8.15,9.24,10.68,10.58,10.31,10,8.91,8.51];
>> q=[A‘,B‘,C‘,D‘,E‘];
>> w=cov(q)
w =
10.3710-4.7446-6.6023-0.1873-1.8881
-4.744659.150338.7606-3.07433.0982
-6.602338.760628.6966-2.01992.4166
-0.1873-3.0743-2.01990.84740.3936
-1.88813.09822.41660.39361.3412
原文:/xr1064/article/details/42525513