matlab拟合韦布尔分布,Matlab 三参数Weibull分布拟合求解

function  a_b_c = wblthree(x)

% f(x) = b*a^(-b)*(x-c)^(b-1)*exp(-((x-c)/a)^b)

% a ------  尺度参数

% b ------  形状参数

% c ------  位置参数

disp('样本区间及最大值与最小值之比:')

x_range = [min(x) max(x) max(x)/min(x)]

alpha = [0.05]; %置信水平

c = linspace(0,min(x)-1,1000)';

Len_c = length(c);

for i = 1 : Len_c

[a_b(i,:),pci{i}] = wblfit(x-c(i),alpha);

lnL(i,1) = - wbllike([a_b(i,:)],x-c(i));

if a_b(i,2) <= 1

break;

end

end

c = c(1:i);

figure('name','wblthree--参数特征')

[max_lnL,position_max] = max(lnL);

subplot(311)

plot(c,lnL,'r',c(position_max),max_lnL,'rs')

title('c - lnL')

text(c(position_max),max_lnL,num2str(max_lnL));

subplot(312)

plot(c,a_b(:,1),'b',c(position_max),a_b(position_max,1),'bs')

text(c(position_max),median(a_b(:,1)),num2str(a_b(position_max,1)));

title('c - a')

subplot(313)

plot(c,a_b(:,2),'k',c(position_max),a_b(position_max,2),'ks')

text(c(position_max),median(a_b(:,2)),num2str(a_b(position_max,2)));

title('c - b')

lnL_a_b_c = sortrows([lnL a_b c],-1);

disp('遍历位置参数C时的极大似然法参数估计：')

a_b_c = lnL_a_b_c(1,2:end)

disp('样本X最大对数(ln(X))似然值：')

lnL = lnL_a_b_c(1)

a = a_b_c(1);

b = a_b_c(2);

c = a_b_c(3);

f = @(x,a,b,c) b*a^(-b)*(x-c).^(b-1).*exp(-((x-c)/a).^b);

t = linspace(c,max(x)*1.5,500);

y = f(t,a,b,c);

F = trapz(t,y)

y1 = zeros(size(x));

figure('name','wblthree')

plot(t,y,'r',x,y1,'sr')

axis([0 max(t) 0 max(y)*1.1])

text(max(t)/4,max(y)/2,[ 'a = ' num2str(a,'%0.1f') ' ,b = ' ...

num2str(b,'%0.3f') ' ,c=' num2str(c,'%0.0f')],'fontsize',12,'color','r')