高斯分布期望和方差的最小二乘法拟合

 最近拟合高斯分布的期望和方差，我写了个使用最小二乘法拟合的函数，经过测试效果还不错。现在公布源码吧，希望能给需要的朋友一些参考。

 

function[u,sigma] = GaussFitting(x,y)

%====================================================================

% date: 2011/03/26

% created by  hfeng

%参数x,y分别为高斯函数观察值x,y

%高斯函数参数拟合

%高斯函数 y = (1/(sqrt(2*pi)*sigma))exp(-(x-u)^2/(2*sigma^2))   (y>=0)

%剔除数据中y = 0 的情况,ln(y)定义域y>0.

%ln(y) =

%(-1/(2*sigma^2))*x^2+(u/(2*sigma^2))*x+ln(1/(sqrt(2*pi)*sigma))-u^2/(2*sigma^2)

%令 a = -1/(2*sigma^2) , b = u/(2*sigma^2) ,

%   c = ln(1/(sqrt(2*pi)*sigma))-u^2/(2*sigma^2)

%高斯函数转化为 ln(y) = a*x^2 + b*x +c

%经过最小二乘法求出 a,b,c值

%进而求得 u,sigma值

%====================================================================

k = find(y==0);

y(k) = [];

x(k) = [];

lny = log(y);

param = polyfit(x,y,2);

a = param(1);

b = param(2);

c = param(3);

u = -b/(2*a);

sigma = sqrt(-1/(2*a));