clear;clc;close all
format compact
%% 正態分布的擬合
% 生成隨機數
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('原始數據', '擬合曲線', 'Location', 'NorthEast');
title(['正態分布擬合,num=',num2str(num)])
xlabel('x');
ylabel('y');
grid on
saveas(gcf,'pic.png')
%% 輸出擬合參數
a = fitresult.a
w = fitresult.w
xc = fitresult.xc
y0 = fitresult.y0
%% 計算均方誤差
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)
得到對應的參數為
a = 992.6775 w = 14.3208 xc = 28.0562 y0 = 0.1646
均方誤差為
mse = 0.69