Question

如何用MATLAB估计概率密度函数

Answer 1

函数：ksdensity
功能：根据给定的数据，估计概率密度分布
示例：
1. 正态分布
x = randn(1,100000);
[y,xi] = ksdensity(x);
plot(xi,y, 'bo')
% 验证
hold on
yn=normpdf(xi,0,1); % 标准正态分布的概率密度函数
plot(xi,yn,'b')

2. 瑞利分布
x = abs(randn(1,10000) + 1i*randn(1,10000));
[y,xi] = ksdensity(x);
plot(xi,y, 'bo')
% 验证
hold on
b = 1;
yn = zeros(size(xi));
k=find(b > 0 & xi >= 0);
if any(k),
xk = xi(k);
% 瑞利分布的概率密度函数
yp(k) = (xk ./ b^2) .* exp(-xk.^2 ./ (2*b^2));
end
plot(xi,yp,'b')

3. 莱斯分布?
N = 100000;
K = 0.5;
const=1/(2*(K+1));
x1=randn(1,N);
x2=randn(1,N);
x=sqrt(const*((x1+sqrt(2*K)).^2+x2.^2));
[y,xi] = ksdensity(x);
plot(xi,y, 'bo')
% 验证
hold on
sig = 1;
v = 1;
yn = zeros(size(xi));
k=find(b > 0 & xi >= 0);
if any(k),
xk = xi(k);
% Rician分布的概率密度函数
yp(k) = (xk ./ sig^2) .* exp((-xk.^2 + v.^2) ./ (2*sig^2)) .* besselj(0, (xk .*v ./ sig^2));
end
plot(xi,yp,'b')