MATLAB機率密度函數估計

MATLAB機率密度函數估計  2016-03-23 16:12:24

分類： C#/.net

函數：ksdensity
功能：根據給定的資料，估計機率密度分布
樣本：
1. 常態分佈
x = randn(1,100000); 
[y,xi] = ksdensity(x);
plot(xi,y, 'bo')
% 驗證
hold on
yn=normpdf(xi,0,1); % 標準常態分佈的機率密度函數
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')
% 驗證
hold on
b = 1; 
yn = zeros(size(xi));
k=find(b > 0 & xi >= 0);
if any(k),
    xk = xi(k);
    % 瑞利分布的機率密度函數
    yp(k) = (xk ./ b^2) .* exp(-xk.^2 ./ (2*b^2));
end
plot(xi,yp,'b')


3. 萊斯分布?
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')
% 驗證
hold on
sig = 1;
v = 1;
yn = zeros(size(xi));
k=find(b > 0 & xi >= 0);
if any(k),
    xk = xi(k);
    % Rician分布的機率密度函數
    yp(k) = (xk ./ sig^2) .* exp((-xk.^2 + v.^2) ./ (2*sig^2)) .* besselj(0, (xk .*v ./ sig^2));
end
plot(xi,yp,'b')
http://blog.chinaunix.net/uid-20692368-id-5680963.html