MATLAB: How do the initial parameter values “start” work in the Three-Parameter Weibull Distribution

distributionMATLABmaximum likelihood estimatesmleparamspdfprobability density functionthree-parameter weibull distributionwblpdfweibullweibull distribution

Trying to estimate a Three-Parameter Weibull Distribution. In the scripture of Matlab, there is given the following execution:
rng('default') %For reproducibility
data = wblrnd(1,1,[1000,1]) + 10;
custompdf = @(x,a,b,c) (x>c).*(b/a).*(((x-c)/a).^(b-1)).*exp(-((x-c)/a).^b);
opt = statset('MaxIter',1e5,'MaxFunEvals',1e5,'FunValCheck','off');
params = mle(data,'pdf',custompdf,'start',[5 5 5],'Options',opt,'LowerBound',[0 0 -Inf],'UpperBound',[Inf Inf min(data)])
I dont really understand, how the numbers after 'start' work? What relationship do the numbers have to the scale, shape and location parameters? Days spent searching for an answer.. The following picture demonstrates my problem:

Best Answer

Hi,
The 'start' argument in mle method is used to specify intial parameter values to the custom probability distribution function specified by the user. The value of start is also constrained such that it lies between Upper and Lower bounds specified.
In the highlighted case, due to the change of wiebull distribution parameters I guess the min(data) is less than the values of start specified. Thus leading the constraint to fail.
Hope this clears your concern!
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