多维联合正态分布代码matlab（以二维为例）_hsuuuu1的博客_正态分布代码matlab

clc;
close all; clear;
% 多维联合高斯概率分布
%%
% 二维联合概率分布

%方法一：调包
mu = zeros(1,2);     % 均值
sigma = [1  , 0.9; 
         0.9  , 1];  % 协方差
rng('default')  % For reproducibility
X = mvnrnd(mu,sigma,1000);

y = mvnpdf(X,mu,sigma);
figure
scatter3(X(:,1),X(:,2),y, '.')
xlabel('X1')
ylabel('X2')
zlabel('Probability Density')
%%
%方法二：直接上公式
mu2 = mean(X);
sigma2 = cov(X);
sigma3 = (X-mu2)'*(X-mu2) / length(X);  % 用公式计算协方差 E[(X-mu)'(X-mu)]

y2 = sqrt(1/((2*pi)^length(mu2)*det(sigma2))) * exp(-1/2*(X-mu2)*inv(sigma2)*(X-mu2)');
y3 = zeros(1000, 1);
for i = 1: 1000
   y3(i) =  y2(i, i);   % 这里是重点！
end
figure
scatter3(X(:,1),X(:,2),y3, '.')
xlabel('X1')
ylabel('X2')
zlabel('Probability Density')

clc;
close all; clear;
% 多维联合高斯概率分布
%%