Does the values of "start" effects the estimation of the 3 parameter weibull distribution

To estimate the 3 parameter weibull distribution, matlab needs start values. You can read here:

https://de.mathworks.com/help/stats/weibull-distribution.html

I am generating random numbers with 3 parameter weibull distribution and estimating them with MLE.

For that, I need to give start values.

params = mle(data,'pdf',custompdf,'start',[5 5 5],...
     'Options',opt,'LowerBound',[0 0 -Inf],'UpperBound',[Inf Inf min(data)])

Does anybody tested different startvalues? I tested a lot of start values. I used "rng(default)" to have the same "random" numbers every run and checked the results, if something changes.

Sometime the results changes a little bit, sometimes nothing changes. So do someone checked the startvalue much more accurate?

Answer 1

[Pratyush Roy]

Hi Mustafa,

The mle function uses the “fminsearch” or “fmincon” options to maximise the mle parameters iteratively. The ”start” parameter refers to the initial set of values for the parameters and it changes with every step of the optimization process. A poor choice of starting point can cause mle to converge to a local optimum that is not the global maximum, or to fail to converge entirely.

Since the dataset generated by picking random samples from a Weibull distribution, the optimization leads us to the proper estimates irrespective of the initial condition. However, if we try to fit Weibull distribution to any arbitrary data, this might cause problems to achieve convergence.

You can refer to the following links for further help:

https://www.mathworks.com/help/optim/ug/fmincon.html

https://www.mathworks.com/help/optim/ug/fminsearch-algorithm.html

Regards,

Pratyush.