what's wrong with my ks test?

I get too high D-values with my ks-test but at the same time low p-values. How is that possible?

C = wblrnd(100,1);
C = C';

% 3 parameter WEIBULL SETUP
custompdf = @(x,a,b,c) (x>c).*(b/a).*(((x-c)/a).^(b-1)).*exp(-((x-c)/a).^b);
customcdf = @(x,a,b,c) (x>c).*1-exp(-((x-c)/a).^b);

opt = statset('MaxIter',1e5,'MaxFunEvals',1e5,'FunValCheck','off');
params = mle(C,'pdf',custompdf,'start',[mean(C) std(C) min(C)],'Options',opt,'LowerBound',[0 0 -Inf],'UpperBound',[Inf Inf min(C)]);

a_Welle = params(1,1);
b_Welle = params(1,2);
c_Welle = params(1,3);

x = [c_Welle+eps(c_Welle):0.1:max(C)*mean(C)];

% 2 parameter WEIBULL SETUP
p = wblfit(C);
[nlogl,pcov] = wbllike(p,C);
[quantile_Wbl2,q95lo,q95up] = wblinv(0.99958333,p(1),p(2),pcov);

Q = quantile(customcdf(x, a_Welle, b_Welle, c_Welle),0.99958333);

 
% kolmogorov-smirnov 
[h_wbl3,p_wbl3,ksstat_wbl3] = kstest2(C, customcdf(C,a_Welle,b_Welle,c_Welle));
[h_wbl2,p_wbl2,ksstat_wbl2] = kstest2(C, wblcdf(C,p(1),p(2)));

fprintf('Two parameter Weibull-Distr.: h = %d, p = %f, D-Wert = %f\n', h_wbl2, p_wbl2, ksstat_wbl2);

Two parameter Weibull-Distr.: h = 0, p = 0.289041, D-Wert = 1.000000

fprintf('three parameter Weibull-Distr.: h = %d, p = %f, D-Wert = %f\n', h_wbl3, p_wbl3, ksstat_wbl3);

three parameter Weibull-Distr.: h = 0, p = 0.289041, D-Wert = 1.000000

How can I improve my code?

Answer 1

[the cyclist]

My guess here is that this line of code

C = wblrnd(100,1);

is not doing what you expect. It is generating just one value, from a Weibull distribution with parameters a=100, b=1. Take a look the documentation for wblrnd, to find the syntax for what you want to do. I expect you wanted something like

C = wblrnd(4,3,100,1);

[Kalle]

Owww, how embarrassing! thank you!