---

title: 正态分布与参数估计
categories:

• 杂项
  tags:
• 学习

---

正态分布与参数估计

预处理

clear rng(6331); mu = 1; sigma = 1;

真实概率密度曲线：

fplot(@(x) exp(-(x-mu).^2./(2*sigma))./(sqrt(2*pi)*sigma) ) title("真实概率密度曲线")

四个样本直方图

n_1 = 10; n_2 = 50; n_3 = 500; n_4 = 1000; y_1 = sigma.*randn(n_1,1) + mu; y_2 = sigma.*randn(n_2,1) + mu; y_3 = sigma.*randn(n_3,1) + mu; y_4 = sigma.*randn(n_4,1) + mu; histogram(y_1,10) title("n=10") histogram(y_2,10) title("n=50") histogram(y_3,20) title("n=500") histogram(y_4,20) title("n=1000")

四个样本参数估计值

矩估计==最大似然估计 [mu_, sigma_] =estimate(y_1 , n_1) mu_ = 0.6865 sigma_ = 0.2972 [mu_, sigma_] =estimate(y_2 , n_2) mu_ = 0.7853 sigma_ = 1.0036 [mu_, sigma_] =estimate(y_3 , n_3) mu_ = 0.9213 sigma_ = 1.0244 [mu_, sigma_] =estimate(y_4 , n_4) mu_ = 0.9908 sigma_ = 1.0422

参数估计误差随样本容量增大的变化曲线

矩估计==最大似然估计 样本容量取 10~1000 n = 10:1:1000; dsigma = zeros(length(n),1); dmu = zeros(length(n),1); for i = 1:length(n) y = sigma.*randn(n(i),1) + mu; [mu_, sigma_] =estimate(y , n(i)); dsigma(i) = abs(sigma - sigma_); dmu(i) = abs(mu - mu_); end plot(n,dsigma) hold on plot(n,dmu) legend('△σ','△μ') hold off

矩估计、最大似然估计函数

function [mu_, sigma_] = estimate(y , n) mu_ = sum(y)/n; sigma_ = sum((y-mu_).^2)/n; end

标签：10,randn,title,mu,参数估计,estimate,sigma,正态分布
来源： https://blog.csdn.net/weixin_47102975/article/details/111998646