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How do the initial parameter values "start" work in the Three-Parameter Weibull Distribution?

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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:

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Accepted Answer

Harsha Priya Daggubati
Harsha Priya Daggubati on 15 May 2020
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!

  2 Comments

Mustafa Vural
Mustafa Vural on 22 May 2020
Hi,
why are there three numbers for start? Why isnt it enough to give just one initial parameter value? So, do the numbers have a relationship to the shape and scale parameter?
Harsha Priya Daggubati
Harsha Priya Daggubati on 22 May 2020
The value of the start is used to give initial values for the parameters in your probability distribution function i.e custompdf. I didnot understand what do you mean by shape and scale parameters.

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