MATLAB拟合正态分布
clear;clc;close all format compact %% 正态分布的拟合 % 生成随机数 num = 50; y = randn(1000,1); x = 1:num; y = hist(y,num); xx = x(:); yy = y(:); % Set up fittype and options. ft = fittype(\'y0+(a/(w*sqrt(pi/2)))*exp(-2*((x-xc)/w).^2)\', \'independent\', \'x\', \'dependent\', \'y\'); opts = fitoptions(ft); opts.Display = \'Off\'; opts.Lower = [0 0 0 0]; opts.StartPoint = [1.1 1.1 1.1 1.1]; % Fit model to data. [fitresult, gof] = fit( xx, yy, ft, opts ); % Plot fit with data. figure; plot(fitresult) hold on plot(xx, yy,\'b*\'); legend(\'原始数据\', \'拟合曲线\', \'Location\', \'NorthEast\'); title([\'正态分布拟合,num=\',num2str(num)]) xlabel(\'x\'); ylabel(\'y\'); grid on saveas(gcf,\'pic.png\') %% 输出拟合参数 a = fitresult.a w = fitresult.w xc = fitresult.xc y0 = fitresult.y0 %% 计算均方误差 yyy = y0+(a/(w*sqrt(pi/2)))*exp(-2*((xx-xc)/w).^2); rmse = 1/length(yyy)*norm(yyy-yy); fprintf(\'num = %d, rmse = %.2f\n\',num,rmse)
得到对应的参数为
a = 992.6775 w = 14.3208 xc = 28.0562 y0 = 0.1646
均方误差为
mse = 0.69
