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’)
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