fitting a 3-parameter of Weibull PDF using mle

Hello

I am trying to estimate the 3 parameters of a Weibull PDF on a series of positive values (n=934). My custom pdf is

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

phat=mle(data,'pdf',custpdf,'start',[1 1 1]);

Error using mlecustom>llf_pdfcdf (line 440) The PDF function returned negative or zero values.

Error in fminsearch (line 200) fv(:,1) = funfcn(x,varargin{:});

Error in mlecustom (line 184) fminsearch(llf,start,opts,uncensData,censData,uncensFreq,censFreq,fun1Args,fun2Args,checkFunVals,lb,ub);

Error in mle (line 245) phat = mlecustom(data,varargin{:});

I tested also

 phat=mle(data,'wblpdf',custpdf,'start',[1 1 1]);

But I get only two parameters

Vincent

Any idea about what is wrong ?

Answer 1

[Torsten]

custpdf = @(data,a,b,c) (data>c).*(b/a).*(((data-c)/a).^(b-1)).*exp(-((data-c)/a).^b);
opt = statset('MaxIter',1e5,'MaxFunEvals',1e5,'FunValCheck','off');
phat = mle(data,'pdf',custpdf,'start',[5 5 5],'Options',opt,...
    'LowerBound',[0 0 -Inf],'UpperBound',[Inf Inf min(data)])

Best wishes

Torsten.

[Vincent Moron]

Thanks for the quick reply. The solution does not converge. I tried to increase the MaxIter but it still does not converge. So perhaps my data does not fit with a 3-parameter Wdl CDF ? I attached the data I am trying to fit

Answer 2

[Jeff Miller]

Cupid ( GitHub ) says the ML estimates are Weibull(468169.4353,0.92433,11159.7031), obtained with:

mydist = Weibull(400000,.9,min(data));
mydist.EstML(data);

There don't seem to be numerical problems even though the numbers are so big. The following:

dataover1000 = data / 1000;
mydist2 = Weibull(400,.9,min(dataover1000));
mydist2.EstML(dataover1000)

gives the corresponding Weibull(468.1694,0.92433,11.1597).

Note that the estimate of the 3rd parameter is always the minimum of the data.