MATLAB拟合正态分布

时间：2021-07-30 00:22:17
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)

　　MATLAB拟合正态分布

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

　　

相关文章